Afrotech has put together a great video that demonstrates the basics of replacing a capacitor. This is normally only important when repairing old electronics, however recently there have been many cases where faulty capacitors fail after only a few years (or less) and need to be replaced to keep the device operational. Dell is one of the computer manufacturers who had a bad issue with defective capacitors. In this case replacing a dollars worth of capacitors could bring your dead computer back to life. The one piece of good news is that the capacitors we are talking about here are the large electrolytic type which are almost always through hole soldered so they are simple to replace with minimal tools and experience.
We have featured the work of Afrotech here before, remember those cool hard drive speakers? His speakers were a big inspiration for the Hard Drive Oscilloscope that I built back in 2006. Once you are done watching the above instructional video be sure to watch the video of magic smoke being let out of lots of capacitors and other components.