I can tell you how I do it, but I do know there are multiple ways and a bunch of tools.
I have a little block of foam, to save my from poking my legs, or a table if I'm not working on my lap. I have wool batting (undyed, core wool and dyed wool). I start with the core wool to get the shapes I want, then add color after. I have a few different size/shape needles, but the one I use most is the yellow needle from Felt Alive. The needles have notches on them, so when you poke the wool, it catches some of the fibers and tangles them. They have regular and reverse notch needles (to either tangle the fibers to make a shape, or to pull fibers out and make fluff).
You poke a lo, adding more wool here and there until the shape is what you want. You can make seperate parts and attach them, which is what I do, or use a wire armature and felt over that.
It's time consuming, but loads of fun!