Ascension Systems

Frog
One ascender is at chest level (usually a Kroll [Petzl]) and is attached between the user's chest harness and sit-harness. Another ascender above it is attached to the user's harness and to a long loop for both feet and is operated by the user's arms. Movement up the rope is made by repeated movements of the foot-loop ascender up the rope, pushing up with both feet together and then sitting on the chest ascender. At the beginning of the climb, it's necessary for the user's feet to clamp the rope until there is sufficient weight to pull itself through the kroll (this is usually called self belaying).

Split foot frog
Same as the frog (above) except with the addition of another ascender like a Pantin [Petzl] on one foot, and instead of the leg loop coming from your top ascender holding both feet, it only attaches to one foot. The advantages are that you don't have to self belay, you can use your feet independently of each other (you can use one to push yourself away from the wall if necessary also), and you have a third point of contact when crossing a knot or rebelay. Frog systems are usually one of the slower methods, but because they offer such a good resting position, they are used a lot on longer drops. Frog systems are also the easiest systems to cross knots and rebelays with.

Rope Walker
Rope walker systems usually have one ascender attached to each foot (two ascenders total): one slung slightly above the foot and one slung about waist level. The two ascenders are attached together via a rope (that is strung through a piece of tubular webbing to reduce friction on the back of the neck) that runs from the top of one ascender behind the user's neck and attaches to the top of the other ascender. The motion of stepping up on one ascender pulls the opposite up the rope and vice versa. The user is usually attached to the rope via a specialized pulley attached to the chest harness. The user might or might not have a hand operated ascender attached at the waist harness, however, most people find that the hand operated ascender slows them down (it is a good idea to have one available though, even if it isn't attached to the rope).

Texas Rope Walker
A modified rope walker system that has one of the ascenders attached to the foot (not slung) the other is slung from the foot about waist level. The one slung from the foot is attached to a shock cord (usually strung through a piece of tubular webbing again to reduce friction) and the shock cord is attached at the back of the chest harness and is slung over the user's shoulder. The rest remains the same. Both rope walker setups are definitely the fastest, but they are very hard to cross over knots and rebelays with.

Monkey Method
This method uses two hand-operated ascenders, each of which is slung with a loop to the corresponding leg and attached to the user's harness (to take their weight if need be). To ascend, you move your right arm and right leg up in unison, then your left arm and left leg in unison. This method is the most simple, but least efficient. It's good for short climbs.