There are many ways of taking fur from a hare's mask, but I find it saves time if you "process" your dubbing all at once (it also saves space, too). Basically, you need to remove all the hair & fur from the mask & mix it together. Traditionally, different parts of the mask are used for different flies, like the Hare's Ear Nymph for example, but I'm personally not that picky about it. However, using & blending the material from a hare's mask will get you dubbing that has a good mix of soft fur & guard hairs, as well as a nice mix of light & dark shades.
Below is a short video showing a quick & easy method for harvesting the hair & fur from a hare's mask & how to mix everything together. This is pretty much the method I use & I know that, for me, it works quite well.
Now, if you want to change the color of that dubbing by dyeing it to a particular color for a specific insect pattern, that's a discussion for another day & I'll show you some methods for doing that soon. For now, let's just get the hair off the hare........