Edging is an exercise in precision. Many edges are so small they can't be seen until you're at them. Careful placement of the foot is essential, and once the shoe is weighted it is likewise essential not to change the attitude of the shoe lest you pop off. In short, knowing how to keep your foot perfectly still on the edge while the rest of your body carries on. Contary to common sense, a razor sharp shoe edge is NOT ideal for standing on small holds.
Most shoes feature a sole that is beveled back underfoot, resulting in more stable edging.
If applicable, use the rest step whenever you have to stop to place protection or when you need a rest. Imaginative resting is one of the keys to efficient climbing. Don't move your foot until you know exactly where you're going to put it. When possible, place your feet directly beneath your hands to minimize the strain on the upper body. Concentrate in the hold as you bring your foot to it.