The first thing to check with Ubuntu is to go to (*fires up the remote VM to double-check where*) System|Administration|Hardware Drivers, and check if Ubuntu can install them for you (not sure about Realtek, but it's usually pretty good about that sort of thing, although they are sometimes out of date). If it can't, then please post a link to the file you downloaded, as well as the tutorial, and I'm sure either myself, or whoever gets to it first can help you out.
If you found a source tarball (e.g. *.tar.gz or *.tar.bz2), then here's the gist of what you'll be doing. Most drivers (modules) are packaged with the kernel. However, due to licensing, some aren't allowed to be packaged and distributed that way. In some cases (e.g. ATI), they have a nice binary that you download, and it packages them up for you. In other cases, you have to take the module source, and compile it against your running kernel version. This involves downloading the kernel header files (or occasionally the full sources), and doing some console-fu. It's not all that hard (if things go well), but you have to know what you're doing. In either case, I'm sure we can walk you through it.
P.S. learn to love the console, and it will become your best friend :D
-Jeff