What can I do to make my computer faster?

There are a number of ways you can make your computer faster. These break down into two major categories, software, and hardware.

Software Solutions:

These solutions will improve the performance, but will only get it running as fast as it did when you purchased it.

Defragment your hard drive.
Stop any unnecessary programs from loading when your computer boots. *If you are not comfortable doing this on your own, have a professional take care of this for you.

If you would like to increase the speed of your computer, the easiest method is to add RAM (memory) to your computer. Adding RAM can cause a noticeable improvement in the performance of your computer. The type of RAM your computer takes will depend on the age of your computer. RAM prices have dropped significantly in the past few years, making this one of the most easily justified upgrades on most systems.
Replacing your hard drive is another way to increase the performance of your system. *The primary purpose of replacing your hard drive is usually to add storage space. New hard drives are larger, and faster than old hard drives.
If you are looking for more performance than RAM alone can add, you are looking at a major overhaul. To substantially increase the speed of your computer, you will need a new processor. As technology goes, new processors require new motherboards, new RAM, and usually a new video card. This is OK, because all of these other new parts will also improve the performance.
This kind of upgrade is not always worth it. You will still have some old parts on your computer, and sometimes you are better off just replacing the whole computer.