The basic point behind take off is simple. Get the airplane in the air without crashing into anything! There are a couple of standard ways to do this:
The standard way to take off is fairly simple. Advance the throttle to full, and start off down the runway. Once your speed has sufficiently built (this should be your Vy speed) you pull back slightly on the stick, and raise the nose gear off of the runway. The airplane should, at this point, fly itself off the runway and into the air. Keep the airspeed at that Vy speed until you have finished climbing.
To Clear a Fifty Foot ObstacleEdit
Climb out at Vx, to clear a 50 foot obstacle at the end of the runway.
With a soft field take off, the aircraft needs to get off the ground as soon as possible. Adjust flaps to 10degree, full aft on the yoke, and advance throttle full. You will prematurely lift off due to ground effect. Stay within ground effect (about the length of your wing span), and build your speed to Vx. Climb out at Vx.