Let's start with the acronym SETI -- it stands for the Search for Extraterrestrial Intelligence. This search involves the use of large radio telescopes. Using these telescopes (which are essentially extremely large satellite dish antennas), scientists involved in SETI hope to detect radio signals "leaking" from other intelligent civilizations or that other civilizations have specifically beamed at us.
The basic principles behind SETI rely on three assumed facts:

1. There must be other intelligent life forms out there. The Milky Way galaxy alone contains billions of stars like our own sun, and the universe contains billions of galaxies. If intelligent life can evolve in one place, then presumably it can evolve in many other places as well.
2. Any intelligent civilization would discover radio waves and begin leaking them into space. Humans, as an intelligent life form, discovered radio waves fairly early in our development, and we have been leaking radio signals in significant quantities for much of the 20th century. We leak signals in everything from AM and FM radio broadcasts to TV broadcasts to all sorts of satellite and radar broadcasts. Every time you open your garage door, you leak a radio signal into space!
3. Any intelligent civilization would realize that there might be other intelligent civilizations, and it might try to send high-powered signals right at us. Humans have, in fact, tried this in several different ways. If you can find a copy of Carl Sagan's book entitled Murmurs of Earth, it offers a great introduction to what we have tried (everything from radio broadcasts to phonograph records attached to satellites!).

If either the first or second assumption is invalid, then SETI is a hopeless waste of time. If they both turn out to be true, however, then it is only a matter of time before we detect something! The problem with SETI is that it requires massive computational resources. Imagine having a radio that can listen to every radio, TV, radar, satellite and garage-door-opener frequency all of the time. The SETI approach narrows it down a bit, but it is still listening to a huge number of frequencies. Then, the computer has to look at each frequency separately and try to decide if it is carrying an intelligent signal as opposed to noise.
To give you an idea of the scope of the problem, the antenna used for SETI@home records 35 gigabytes of data every day. According to the SETI@home site, the average home computer takes about 30 hours to process one "work unit," and the 35 gigabytes of daily data is broken into 140,000 work units. That's 4.2 million hours of computation time just to process one day's worth of data!
Buying that amount of computational power would be incredibly expensive, so SETI@home comes up with an absolutely ingenious way to create that computing power out of thin air. When your computer is idle, it displays a screensaver. In most cases, a computer displaying its screensaver is doing absolutely nothing. All the computing power available in your machine is being wasted. So SETI@home created its own screensaver, which you install on your machine. With the SETI@home screensaver installed, your computer actually processes SETI data when it is idle. The screensaver downloads a packet of data containing a work unit of radio signals and then grinds away on them. When it's done, it sends the results back and gets another packet. The screensaver, instead of displaying fish or flying toasters, displays the work in progress.
If you would like to donate your computer's spare cycles to the SETI cause, you too can join SETI@home! Take these three steps:

1. Go to the SETI@home home page and download the software. The file is about 800 kilobytes, so it doesn't take very long to download.
2. Install the software. It takes about 30 seconds -- this is one of the easiest installs I have ever seen!
3. Join the HowStuffWorks group by going to this URL: http://setiathome.berkeley.edu/team_display.php?teamid=62

You will be amazed as you watch your computer grinding away in the attempt to find other intelligent life forms!