Our materials: the fur to be dyed (in this case Monterey Mill's white fox), acrylic paint (artist's quality paint is preferred), a container to mix it in (a paper dixi cup), and something to mix it with (a plastic spoon), plus a table that you can get dirty/a container large enough for the fur. You'll also need a slicker brush.
Mix up some of the paint with water. Insure you break up all the lumps or that will affect the fur later on. The consistency doesn't matter as long as it's easily pourable.
Flip the fur so the backing is facing up and pour the paint on . Try to cover as much area as you can from edge to edge.
Then fill up your container with water and then pour it on as well. Too much water will dilute your paint more than needed and not enough will result in the paint not covering all of the fur. Use your best judgment.
Now grab the fur and 'mix' the paint into it. Roll it up and squeeze out the paint and then mop it back up into the fur. Don't try to 'rub' the paint in but just gently use the water to carry the paint pigments to the undyed area.
Once there is no white fur left, lay it fur side up and brush out the fur with a slicker brush. It will be drippy so lay it out flat to keep the water pooled in and around the fur.
IMPORTANT: Do not squeeze out the water - the water carries the paint and you need it to dry by evaporation so it leaves the paint behind as it dries.DON'T hang it up or lay it on a grate where the water can drip out.
Then as it dries, occasionally brush out the fur so that it does not clump. If you have any clumps of paint, get rid of them or the fur there will dry hard like a rock and you'll not be able to remove them later.
For deep colours, one coat will not be enough. Once the paint has dried fully and cured for a few days, you can repeat the process for a darker result. Do this as many times as you want though the fur will of course get a bit rougher the more paint that is in it.
EDIT: The finished tail using the new blue fur:
crossposted fursuit and beetlecat