RIT Dyes are chemical dyes which are available in both a powder dry form as well as a liquid form.  I use the dry dyes rather than the liquid dyes because the dry dyes store better over a long period of time, both work equally as well. RIT Dyes are available at most grocery stores.

Take a 1 quart glass jar and add 3 cups of water

Add 1 tablespoon of dry dye 
(you can mix colors for a varied palette)
If you use liquid RIT dye use half the bottle (4 fl.oz.)

Add 3 tablespoons of white vinegar to help set the dye

Fill a large sauce pan 1/2 to 3/4 full with water

Place the uncovered glass jar in the sauce pan on the stove 

Heat the water in the sauce pan to boiling, then lower the temperature to a simmer. Watch the dye mixture to make sure it does not boil.

Roll your twisted horsehair pulls into the jar 
(you can dye up to 100 pulls at a time using this method)

Make sure all of the pulls are submerged in the dye

Stir the mixture frequently to make sure the pulls are dyed evenly

Use a wooden or plastic spoon to stir the dye mixture

The dye takes very quickly, sometimes in only a few minutes, so keep a close eye on it.

Leave the hair in the dye until it is a little darker than you want your final color to be. (the final color will be lighter after you rinse)

Remove the pulls and rinse under warm water until the water runs clear. To make sure the horsehair is completely rinsed leave the pulls in clean standing water for 10 min. If the water is clear after that time the hair is fully rinsed. With some darker colors you might need to do this step several times. If your pulls are not rinsed properly the colors can bleed later.

Lay your pulls out on a towel or hang them with plastic clips to dry

Allow your dye mixture to cool before putting the lid on the jar. 

Your dye can be stored for future use. 

If you would like more information about RIT dyes go to their web site at www.ritdye.com

They also have a page on how to mix RIT dyes for certain colors www.ritdye.com/b.asp