If you're already adept at turning your hip into the wall as you climb, you should be able to use the drop-knee technique without much difficulty. Often used on overhanging routes, drop-kneeing is the act of twisting one knee to the inside. This is often accompanied by twisting the hips upward and pushing with the foot to gain upward mobility.
Flagging is the act of extending one leg outward to counterbalance the body. This is used in situations where the body would otherwise swing, or "barn door," away from the wall on one side.
Used to create friction between the wall and your shoe, smearing refers to placing the sole of your foot directly against the wall rather than on a hold. Smearing is useful on more difficult routes with fewer holds, or when holds are far apart. Smearing is a difficult maneuver that requires balance and flexibility, but mastering this technique will often allow you to move through the crux of a difficult route.
You may have noticed that the back of the heels on your climbing shoes are covered in the same sticky rubber that is used on the soles. This allows you to hook your heel onto a hold that is too high to toe down on. Heel-hooking enables you to pull your weight up with your leg.
Mantling is the act of pushing yourself up by pushing straight down on the palm of your hand, similar to pushing yourself out of a swimming pool. Mantling is often used to bring your foot up onto the same hold that your hand is on.