Accelerating sounds easy enough: twist the throttle and hold on... let's see!
To accelerate from a stand-still, yes, you let in the clutch while at the same time, roll on the throttle. The weight should be forward on the bike, to compensate for the front wheel coming up.
Moving from side to side is very important when accelerating hard: the rear wheel will have the tendency to either deflect on rocks etc or just slide side to side under hard acceleration. To compensate, you must be ready to move your body side to side. Watch some motocross starts to get an idea.
While cornering, there's quite a few uses for acceleration.
Coming out of the corner, you normally want to pick up speed again, so you'll get on the gas, taking care to keep the bike pointed where you want to go and the rear wheel tracking that. If you get on the throttle too hard, the rear will come around: oops!
In fast sweepers, to keep the speed, you can get on the throttle and slide the rear wheel through the turn. This is most fun to watch on a supermoto track.
In tight turns, you can use the throttle, to slide the rear out, instead of the brakes. This is a good skill as you pick up speed in the woods.