Takeoff
While taxiing, apply full back pressure on the yoke (pull it towards you) to relieve the pressure on the nose wheel. Keep the braking to a minimum as much as possible so you can keep your inertia.
Hold short before taxiing onto the runway and look for traffic approaching to land. Lower the flaps to 10°. When all is clear, radio the tower or announce your intentions on the Common Traffic Advisory Frequency (CTAF).
Once you have obtained clearance, taxi onto the runway and align on the center-line.
Do not stop. As soon as you are lined up, smoothly apply full power and continue to hold the yoke back.
The nose will begin to rise. Continue to hold back pressure to keep the nose wheel off the ground. The cowling should be aligned with the horizon.
The plane will takeoff on its own. Quickly, but smoothly, apply forward pressure to lower the nose. The plane is off the ground but does not have enough lift to fly. This is called Ground Effect. The plane is literally flying on a cushion of air between the wings and the ground. If you go too high, you will lose this cushion and crash. Try to keep the altitude approximately equal to your wingspan.
As the speed increases, you will need to apply even more forward pressure on the yoke.
Once you reach a safe airspeed (usually the best rate of climb or Vy), raise the nose and climb at your best rate of climb. This information can be found in your Pilot's Operating Handbook (POH).
Landing
Enter the pattern as you would at any airport after contacting the tower or announcing your position on the CTAF.
Fly the standard traffic pattern, beginning your descent on the downwind leg abeam the touchdown point of the runway. Don't forget to lower 10° of flaps.
When the runway is 45° over your shoulder, turn base and lower another 10° of flaps.
Turn final to align the plane with the runway and lower flaps completely (30° or 40° depending on the aircraft).
Once you are a couple feet above the runway, gently flare and add a little bit of power. Adding a little power at this point allows you to touch down at a slower airspeed.
As soon as the main gear touches the runway, pull the power back to idle.
Apply full back pressure on the yoke to keep the nose wheel of the ground. Allow it to settle on its own.
Holding full back pressure, taxi off the runway to make room for other traffic. You may need enough speed to avoid settling and getting stuck - use caution!