Though there are shortcuts, like Hal said, the best way to improve your time is with practice. My beaver skinning time has gone from 1.5-2hrs(just hide) down to 30-45 minutes (including the meat).
Proper tools help, too. My first year I was using a $0.99 paring knife, that actually holds a pretty good edge. The next year I bought a beaver knife and that cut down my time quite a bit, and also saved a couple of knife cuts in the pelt. This year my wife bought me a skinning knife for my birthday, and that cut down time on everything as well. Something else I've noticed that helps is what I call the Wyoming style knives (I've seen them advertised as tail zippers). If I can get it underneath the belly of a beaver, that cut can be made pretty straight, pretty easy, and pretty quick. Sometimes I can't, but I always try.
The trough helps out quite a bit, but a table works fine, too. If you use a table, nail or screw a block of wood to a portion of it. This gives you something to hold the head when you skin that portion out, and keeps the weight of the hide from pulling the carcass off the table.
I'm not an expert by any means, but these are a few things I've picked up and done over the last few years. Good luck.