I thought I'd describe how I make a wig from Tibetan lamb. I'm sure there are other ways, I just haven't figured them out yet. I start by draping a paper towel over the doll's head. Pinch darts in the paper towel to get a good fit. Pin the darts and trim the paper towel so it matches the natural hairline. I like to fold under the front edge of the wig to make a nicer hairline at the face, so take that into account if you want to do that. Remove the paper towel, cut the darts so there's a seam allowance of about 1/8 inch, and use this piece as a guide to make a pattern with a little more symmetry.
Now use this new pattern to make a cap of felt, and sew the darts with your sewing machine. Fit the felt cap to the head. Does it work? If not tweak it (it's more cost effective to test the pattern with felt than to just cut into your hide).
When you're satisfied with the fit of the felt cap, you're ready to cut the wig from Tibetan lamb. Pay attention to the natural direction of the hair on the hide. I try to position the pattern so the hair flows away from the face. If you've made the pattern piece from freezer paper, just iron it to the hide. Take great care when cutting the hide, to avoid cutting the hair.
I just made a wig for a doll class - I'd already packed all my scissors, so I found a scalpel - specifically, a pointed #11 blade. I drew around the ironed-on pattern with a pen, removed the pattern from the hide, and cut along the line with the scalpel - not flat on the table, but holding the hide up a little. It worked much better than the scissors, and didn't cut any of the hair (nor did I cut myself). While I have easy access to scalpels at work, I don't see why an exacto knife wouldn't work.
With a 1/8 inch seam allowance, sew the darts right sides together, sliding as much of the hair fibers out of the seam allowance and to the right side of the wig as you can. Sometimes the hide doesn't slide well in the sewing machine, so I put the hide on a piece of tissue or pattern paper, sew the dart, then tear the paper away.
For my Verity doll with most of the head painted, this wig needs to be glued onto the head. I glued the front edge of the wig under about 1/4 inch. Fabri-Tac works well, as does Grrrip glue. When that sets, glue the wig to the head with white tacky glue. That glue will give you a little more time to position the wig.
If the doll is all cloth - that is, the head isn't painted - the wig can be ladder stitched in place. Don't glue the front edge under. Just use a fine but strong needle to sew the wig to the head. The cut edge of the wig will be turned under as you go - all the way around the head.
After attaching the head (and all the glue has dried), comb out the hair. This makes it super fluffy and frizzy. Carefully wet the hair (don't saturate the hide) and towel it dry. Add a tiny bit of hair mousse, then comb it out again, styling it a little, then let it dry. All the pretty little curls of the Tibetan lamb come back.