A pretty good article here: http://www.flyanglersonline.com/flytying/dyingmaterial/index.html
Do a google search for "Veniards fly tying" to see the product line. I have dyed fur successfully, but have only dyed biots when it came to feathers. I just used RIT dye on white goose biots (you can buy about 20 biots at craft stores for aqbout what you'd pay for 4 at a tackle shop [sorry Rick]). For furs, I use a hair "lightener" called Blondissima first to bleach the fur and then use a good grade fabric dye for the colour. Works very well for me.
I have done a bit of dying of fly tieng material.
All my experience is with Veniards dye.
It is a bit finicky at times, but that is to be expected with natural materials.
First of all with all materials you need to clean them very well.
Veniards makes a great product called Venpol that is a type of liquid detergent.
Failing that a good quality dish soap will work.
Using warm,that is water you can keep your hands in,add soap according to directions or about 1/4 cup to the gallon of dish soap. Add feathers or fur first,then stir in the soap.
This should soak at least overnight,or better 24 hours. Agitate the works every couple of hours. Do at least two cool water rises and two warm and warmer rinses to get all the fat and/or oil out of the material to be dyed.
Now, I highly recommend with waterfowl feathers to do the whole thing twice. You have to remember that it is the oil in the feathers that keeps them dry, so it is a bit harder to get it all out.If you don't the results will not be very good.
When all that is done have all your other gear ready to go.
Stainless or enamel pot.
Thermometer. Digital with alarm is excellant.
lots of paper towel
hot plate or stove.
lots of time.
Pen and paper- write down how much and how long.And temp.
Add dye and fixer- usually vinegar
now add material wet but wrung out of excess water.
Temp should not go over about 150 F
125 to 135 is excellant- remember the alarm on the thermometer, set it for 5 degrees less than your max.
You have to know that all the dyes are a combination of 3 colours and they all fix at a diferrent rate.
Lighter colours are usually quicker.
Some dark colours take hours. I did a batch of polar the other day that took 9 hours !
When the material is getting close check it frequently.
Take a piece out and rinse.Look a it under natural light. Remember it will dry a shade or two lighter.
If happy take material and rinse two or three times in warm water then twice in cold to get rid of all the fat and extra dye.
Strain your feathers and blot all the extra water.
You can either let them air dry now, or depending on the feather type you can put them in an old pillow case and toss it in the dryer on cool air to speed it up.
Don't let the dye bath get too hot or you will burn the tips of the hair or feathers.they could also curl,both not good.
Try small batches with your buddies material first.
Afer you get a few batches under your belt, you will get a feel for it. Just remember if you screw it up it can always be dyed black.
Speaking of black, to do it right you have to dye the material twice.The first time should be brown or red, depending who you talk to.If you don't it will almost always come out with very dark blue high lights. If you hold it up to the light it will apppear dark blue.