Pruning cuts are made near a growth bud. The resulting growth will vary depending on the bud. If your pruning is to have the effect you want, you'll need to learn to recognize three different growth buds.
A terminal bud grows at the tip of a shoot and causes the shoot to grow longer. These buds produce hormones that move downward along the shoot, inhibiting the growth of other buds on that shoot.
Lateral buds grow along the sides of a shoot and give rise to the sideways growth that makes a plant bushy. These buds stay dormant until the shoot has grown long enough to diminish the influence of the hormones produced by the terminal bud, or until the terminal bud is pruned off; then they begin their growth. If you remove lateral buds, you'll redirect growth to the terminal bud; the shoot will lengthen dramatically and tend to grow upwards.
Latent buds lie dormant beneath the bark. If a branch breaks or is cut off just above a latent bud, the bud may develop a new shoot to replace the wood that has been removed. If you need to repair a damaged plant, look for a latent bud and make your pruning cut above it.
Important tip: Unless you are shearing a hedge, don't make random cuts into a stem or branch. Though results vary, the stem often dies back from the cut to the next growth bud. At the very least, you'll get erratic growth patterns; at worst, the entire plant may die. Even if you make only a few such cuts, groups of long sprouts may emerge from each one, making for an unsightly-looking branch.