What kind of information does a web beacon retrieve?

A web beacon can pass along information such as: the IP address of the computer you are using when you view the beacon, the time of day that the beacon was viewed, the lengh of time you viewed it, and it can also set cookies.

How do I know if there is a web beacon on a given website?

The number one way to tell if a site has a web beacon is to look at its source code (done by right clicking on the webpage and choosing "View Source" from the menu). If the source code contains IMG tags that load from a different server than the rest of the site does, then it contains a beacon.

How do I get rid of it?

If you turn off your cookies, a beacon can't track you. You have to do this when you open your browser. If you decide to use a different computer to access the site, then you have to turn off the cookies on that one as well. The beacon is still there, but it will only account for an anonymous user. It won't get any of the aforementioned information from you.