For those of you who have never cleaned the inside of your computer, you should do so periodically (more frequently if you happen to live in a particularly dusty area). Before you even open the case, disconnect your power supply cord from the back of the computer (while it's off, of course) and if you have one, shut down your power supply unit by flipping its switch (I think most PSU's have one). Press the power button for a few seconds to discharge any remaining electricity and then proceed to open your case. Be sure to ground yourself to before you touch any components (this can often be achieved simply through touching the metal case or by wearing a special wrist band).
With your case now open, you will see the guts of your computer and the many dust dragons (because bunnies are too small) that reside within. The picture to the side is what my own computer looked like after dusting. Not a perfectly clean computer, but much cleaner than it was when I opened it. A can of compressed air and Q-tips will be your best friends for cleaning. And a vacuum cleaner to pick up the tons of dust that will come out. Note that when using compressed air, do not tip it. Getting any kind of liquid in the guts of your computer will be very bad. Also note that when cleaning your fans, do not let them spin freely. It's possible for them to create a kind of static discharge and inadvertently toast your components.
When cleaning, just take your time and try to be as thorough as possible. Your main points to target should be the fans (dust buildup slows the blades), power supply box (always a good idea to keep that as uncluttered as possible), graphics card fan, and your CPU fan (the CPU can get quite warm under heavy operation, so a nice, well-cleaned fan is helpful). I used a vacuum cleaner for removing dust from bare areas (such as the bottom of my case). If you choose to use a vacuum cleaner, be very careful not to touch any key components as the static from the cleaner can fry them.
Once you're all done, make sure you reassemble your case, hook everything back up, plug in your power cord, and turn on your power supply. Good as new and cleaner. You might even notice that the fans will run a little quieter now...