Whitening toothpaste (paste, not gel), Dawn Dish Detergent, OxiClean, CLR, and Rit Rust Remover can all be used to remove tail rust.  The power of cleaning chemical you choose will depend on the severity of the rust stain.  Any chemical treatment to a pony's hair usually leaves the hair needing a wash with Dawn dish detergent and a conditioning treatment.  Be extra careful to thouroughly rinse all chemicals off the pony's body and wash with Dawn as needed.  It's best to try the whitening toothpaste first, as it is often all that is needed and will allow you to avoid harsher chemicals.

Most collectors choose to remove the metal washer and clamp from the pony's tail, to prevent them rusting again in the future.  Leave the clamp on while you're cleaning the hair, so that the tail stays together.  Once finished, remove the clamp using needle nose pliers.  If you replace the clamp with a plastic zip tie, you won't need to worry about rust again.  You can hold the tail in place with a dab of craft glue, or replace the metal washer with a nylon or rubber one.  These washers and zip ties can be found at any hardware store.
Most common in beddy-bye-eye babies and newborn twins, pony mohawks can be persistent and annoying.
To tame pony mohawks, wet the ponies hair, pull it down around the neck, making certain it is smooth, spray with hairspray as needed.  Fold a piece of paper towel over a few times and wrap it tightly around the neck/hair.  Secure it with tape.  Let the pony sit until the hair is dry, then remove the paper towel.
This Re-Curling tutorial by Whippetluv is one of the best I have ever found:

"With a few exceptions, most pony hair is made from nylon fiber, a synthetic material that, when heated or stretched from over brushing, can become damaged, or frizzy. 

Step 1... Frizzy haired pony 
Step 2... Boil water 
Step 3... Dip hair in boiling water 

Step 4...Lay pony on a flat surface and comb out straight. I usually try to put a towel underneath of it to absorb the water. 

Do step 3 and 4 several times

Step 5... Separate a small section of hair and curl around a cut off straw. Use a bobbypin to keep in place (hint..put the crinkled side of the bobbypin inside the straw to avoid a crimped look) 

Step 6...Put curlers in all the hair. Go ahead and dip in boiling water every now and again. You want hair to remain hot and steaming while doing this. 

Step 7...Leave to dry overnight. Then carefully remove bobbypins and slide out straw from the top. 

Step 8...Enjoy your curly haired pony! The heat of the water changes the plastic and the hair will remain curly! No products needed!"
You can use any shampoo and conditioner to wash and condition your pony's hair.  Everyone seems to have their favorite.  Fabric Softener is also a favorite method for conditioning pony hair.  Some people even wipe wet pony hair with fabric softener sheets.

Some ponies have gotten some really strange stuff in their hair over time.  For more stubborn gunk, try washing the hair with Dawn dish soap or an OxiClean bath.
For colored tinsel only, here's a simple technique that's great if you'd like to avoid using heat.  Tutorial and photos courtesy Bebedasha.  

"Separate a piece of tinsel, grab the end firmly with a pair of tweezers and gently pull the tinsel taut.  Then, gently but firmly pull to stretch the tinsel just a tiny bit before releasing it.  Once finished, trim the straightened tinsel so it's the same length as the pony's hair.

This technique does NOT work on the irredecent-plasticy type 'tinsel', it WILL make it worse. (For example, the type on Styling Ponies, G1 Bridal Beauty/Pony Bride/Princess; G3's like Kimono, Rarity, Desert Rose, Sparkleworks.)"
Includes: 

- Cleaning (washing & conditioning) - Curls (factory curls, re-curling) - Frizz Mohawks - 
- Perfume Puffs - Re-hairing (manes & tails) - Re-pinking Tail Rust - Tinsel (replacement, straightening) - - 
Rit Dye - Choose a shade of pink for re-pinking hair!  The Rit website shows you how to mix different shades.  Rose pink and petal pink have been reported to be an exact match to the original Hasbro pink.  
There are luckily several places you can buy replacement hair.  Each color links to a different one of three popular websites where it can be ordered.
Cleaning
Curls
Factory Curls

Original factory curls are a wonderful thing, but can be hard to preserve.  They're often dirty with stray hairs sticking out.  They can be washed, just be extremely gentle and don't scrub or rinse to harshly.  Smooth down stray hairs with your fingers.

See: Would you wash factory curls?
Re-Curling

There are many methods and tools for curling pony hair.  The one's you choose will depend on the size of curls you want and what temperature of water you're comfortable working with.


Q-tips - Usually used with hot water and pinned in place with a bobby pin.  Makes small, tight curls, cannot be placed in boiling water.

Bobby Pins - Used if you choose to dip your pony's hair directly in boiling water, but this method has been losing popularity.  Roll sections of the pony's hair and secure them with bobby pins.  Be certain the flat side of the bobby pin is touching the hair, as the bumpy side will make the hair crimp.  Dip the rolled hair in boiling water for a few seconds.  Let the pony sit until cool and dry, then remove the bobby pins and style.

Foam Curlers - Come in a variety of sizes so they give you a lot of variety in the tightness of curls you can get.  Use with room temperature water.  Wet the hair, not the curler, as it will take FOREVER to dry if the foam is wet.  Once the hair is dry, remove the curlers and style.

Drinking Straws - Can be used with hot water, but should not be dipped in water that is boiling as they will melt.  Makes tight curls, but they are larger than Q-tip curls.  Hold in place with bobby pins, again make certain the flat side of the bobby pin is touching the hair.  You can also hold them in place with rubber bands, if you prefer.  Wrap the ends with strips of paper towel if you're having trouble with the ends slipping off.
For more problematic frizz, return again to Whippetluvs tutorial:

"With a few exceptions, most pony hair is made from nylon fiber, a synthetic material that, when heated or stretched from over brushing, can become damaged, or frizzy. 

Step 1... Frizzy haired pony 
Step 2... Boil water 
Step 3... Dip hair in boiling water 
Step 4...Lay pony on a flat surface and comb out straight. I usually try to put a towel underneath of it to absorb the water. 

Do step 3 and 4 several times

If you want truly straight hair you are now done. Just stand pony up and comb hair how you want it to stay forever."
Frizz
Heavily applying conditioner and running a thin comb through the hair will straighten most minor frizz.  My secret weapon is Pantene's Relaxed and Natural Collection.  I've removed frizz using this that regular shampoos and conditioners didn't even touch.

With caution, sometimes running a flat iron or clamp style curling iron (set on low) over damp hair will straighten frizz.  Be extremely careful not to melt the hair.  Do not use heat (including boiling water) on color changing hair as it will melt.  Currently regular conditioners are all that is known to be safe on frizzy color changing hair.
Mohawks
Perfume Puff Pony Hair
You can break a lot of rules with perfume puff hair.  You want it to be frizzy, so comb or brush it with whatever you have that makes it puffy, but be careful not to pull the hair out (regular plastic combs are probably your gentlest option).  You'll likely lose some of it, which is ok.  If it's only a little you won't be able to tell.  You can wash and condition their hair with the same shampoos and conditioners you use on your other ponies.  Their hair is supposed to be soft, so use tons of conditioner and leave it in for long periods of time if needed.
Photos courtesy BabyIceCrystal.
Re-Hairing
When a pony's original hair is just too far gone, replacing their manes and tails can make a huge difference.  Dollyhair.com does a great job explaining which hair colors match the ponies' original hair, and AeraCura has also created a pony hair color guide.
Manes

There are sooooo many tutorials available on re-hairing manes that I've decided to provide links to a few of them that use different techniques.  You'll have to choose the one you're most comfortable with.

Tictactoepony uses a needle and thread.

Lady Minty uses a wire.

Everyone must think using a re-hairing tool is self explanatory as I'm having a hard time finding a tutorial on how to do so.  I'll add a link as soon as I find one!
Re-Pinking
This is a compilation of information from this thread at the MLP Arena: Re Pinking.
Photos courtesy Teddy.
Tail Rust
Tinsel
Replacement

The hardest part of replacing tinsel is finding tinsel that is fine enough and the right color.  Try party stores and craft stores.  Get creative, even things like Easter grass can come close.  Once you've picked a color, you can replace the tinsel using the same techniques as doing a re-hair.  If the holes are clogged with glue and hair, you might have to remove some glue to do this.  You can secure the tinsel with the same glue you use to secure a re-hair.
Straightening

Many collectors simply run a straightening iron or curling iron, set on low, through a pony's hair and tinsel to straighten it.  This usually works, but if you need a more in depth technique, here are a couple of things to try.
For any color of Tinsel, here's a tutorial and photos courtesy StrawberryReef.  *disclaimer*  StrawberryReef has had some difficulty getting consistent results with this method, so please use with caution.

"Materials used:
TEST pony (do not try this on your most prized pony or any pony that you aren’t willing to toss until you get the hang of it).
~ Herbal Essence Hello Hydration Shampoo & Conditioner
~ Downey Ultra fabric softener
~ Bounce dryer sheet
~ Wide toothed comb with pointy end for separating
~ Tweezers
~ Scissors
~ Small curling iron

1. Wash hair with shampoo and rinse in WARM/HOT water.
2. Apply conditioner and comb through hair. Do NOT rinse.
3. Apply fabric softener to hair and comb through… hair should feel pretty slimy. 
4. Rinse hair with WARM/HOT water...it's ok to leave some conditioner residue.
5. Separate tinsel from hair (I got impatient and did it without separating and it still worked, but I would think the results would be even better if you are able to just attack the tinsel. I had to go over the tinsel more when it was mixed with the hair)
6. By this time the hair should be just damp, not soaking wet.
7. Separate hair into small sections. While seperating, pull any short/broken pieces of tinsel out with the tweezers (pulling close to the base of the hair).
8. Wet the dryer sheet and pull sections of tinsel/hair through the dryer sheet. You will go over the section of hair approximately 10 times with the dryer sheet until the hair/tinsel is a bit tacky/slimy and should feel like it is covered with conditioner.
9. The tinsel should stretch out straight but you will still feel crinkles when you run your fingers across the section.
10. Run the section of hair through a curling iron set to LOW (I was able to do it on HIGH as well, but I never let the curling iron sit on a section for even a second, the iron was always moving over the hair.). Keep running over the section until you no longer feel the crinkles. (the pic below shows the small tinsel section on the left has already been run through the iron)
11. The section will become stiff and flat. Trim any tinsel that is longer than the hair with scissors.
12. Once you have gone over all the hair, rinse hair completely with COLD water and let dry. (My AFTER pictures were taken at this stage).
13. I thought her hair still felt a little gummy so I re-shampood her and tinsel remained straight. Make sure and use COLD water."

Photos courtesy Mandy85.
Photos courtesy BabyIceCrystal.
Photos courtesy Lancer.
Here's a tutorial courtesy Lunamoth on restoring factory curl.

"Run her hair under warm water. squish a little conditioner in & rinse out gently if you feel like it.

Set her down on her side on a towel and spread her hair out above her head (do this where she can sit & dry without being moved

Separate a tiny section & comb straight through it to get all the knots out. Keep it nice & wet, dont let it dry out. i keep a little bowl of water next to me & dip my fingers in while I do this.
Twist the section **making sure to twist in the direction the curl was going** - if it curled left to right, twist left to right. this keeps the hairs from separating too much while you are letting it spring back

Let go gently & let it start recurling on it's own. it will automatically want to spring back into it's original shape.

Set down the curl gently. It is **very** important to make sure you just follow the way the curl wants to go and you dont try to make your own curl. you just want the existing curl to go back the way it was

Here i've done her whole head this way. I just set them down the way they want to be - which in the case of the Teeny Tinies is kind of the afro-poof-springy look

let it dry without moving. This actually doesnt take too long to dry at all.

i didnt show this step, but when it's dry you take your fingers and kind of crunch the curl gently to make the curl more "natural" and not clumped together. dont touch the curls too much, they will frizz up again. You can position the curls in the direction you want and if some frizz is still there just take a little water on your fingers, run them down the curl, and reposition.

And here is her hair about 30 minutes after i was done

Here are my 3 Littles.... i did Little Giggles' hair just before i did Whiskers'. Little Tabby has beautiful non-frizzy factory curl that i havent touched!
Now, if the hair is dry, clumped, and really frizzed and rough-feeling this will only work minimally. This method is good if all that is needed is combing and de-frizz. i have used some Frizz-Ease with a little success on more seriously frizzed curls, but it can get greasy-looking if you use even a tiny bit too much.

You dont have to heat set this since you arent creating new curls. you *can* use a dryer on low with a diffuser if you want to but i found when i tried that it ended up the same as if i didn't."
Using either powdered or liquid Rit Dye, mix it in a bowl or sink of water. Read the directions on the packaging to decide what proportion of dye per water to use. The more dye you put in, the brighter the pony's hair will turn out, so go easy, you can always add more. For non so soft ponies, comb the dye through the hair, then rinse with hot water. Repeat as necessary until the hair is the shade of pink you want.

You have to be careful not to get the dye on so soft ponies' flocking. You can hold the pony upside down while coming in the dye and rinsing. If you're careful, gravity should keep the dye away from the flocking.

Some collectors prefer to simply dunk the ponies mane and tail in the dye bath, instead of combing it through. The powdered dye reportedly won't stain all bodies, tinsel, and when used in a multi colored mane or tail. Remember, unlike dyeing a body, you won't be leaving the hair in the water for more than a few seconds. It can dye their bodies if you leave the vinyl in contact with the dye for too long.
Body - Hair - Symbols - Misc - Materials