Summarize:

Dead, damaged or diseased wood should be removed starting with the origin of the damage. This may mean cutting an entire large area if it is all damaged or dead. You will know if an area is damaged or dead if it does not have leaves during growing season when the rest of the tree is in bloom. Removing dead or damaged branches is one of the few times it's okay to prune your tree in the spring or summer. If you have sprouts growing down near the bottom of the tree out of the main trunk, these are called "suckers" and are actually part of the root system, not the fruiting system on top. They don't have any purpose on your pear tree. Prune these spouts off right at their origin up against the trunk. If you see any suspiciously straight, vertical sprouts growing from a branch of your tree, that's a "water sprout." They look different from other branches because they occur on main branches, have no curve, are somewhat short, and grow straight up toward the sky. Water sprouts have no purpose on your tree and should be cut at their point of origin on the main branch they're growing out of. Fruiting spurs grow on branches that were originally grown two years previously, so you don't need to worry about them on very young trees. They look like smaller curved branches growing off a main branch, with little bud-like shapes, or fruit buds, at the tip. Fruiting spurs usually take 1 or 2 years to grow fruit. The year after fruiting, another 1 or 2 fruit buds will appear in that spot. After 6 or 7 years, the spur will become congested with fruit buds and then you can prune them to allow new fruiting spurs to grow elsewhere. The only other reason to cut them is if the branch is dead or damaged.
Prune any dead or damaged branches. Cut sprouts coming from the base of the trunk. Remove straight vertical sprouts coming from main branches. Avoid cutting fruiting spurs most of the time.