If you have a CD burner in the laptop, the easiest way to back up your documents is just to copy them to CDs. If you look in Windows Help (Start|Help) WinXP has a "drag and drop" procedure that should work okay for burning files to a CD, although I've never tried it. If your computer came with a burner installed, it probably also came with either "Roxio EZ-CD" or "Nero Burning ROM." I prefer Roxio for data CDs, which is what you want to make, although either should do a fine job.
The only problem you're likely to run into is that long filenames frequently need to get "modified." The legal characters that can be used for filenames on CDs are slightly different than the ones you can use on your hard drive, and a CD cannot have a total path+filename more than a certain length. The length limit is much shorter than is permissible on your hard drive.
Nero will tell you if there's an "unacceptable" filename, but makes you abort the setup and search out the file and fix it, and then start over. Roxio identifies the file much more clearly, and will fix it for you and continue setting up the burn. I'm not sure how the built-in Windows burn procedure handles such problems. If you use short filenames, and don't have deep subfolder levels, you shouldn't have a problem.
If you don't have a burner, you need something you can copy the files to. My suggestion would be a moderately sized external USB-2 hard drive, if you've got more files than you can fit on a few floppies. This will require a bit of an investment, but you need some place where you can keep an archive. Nothing that only exists as single copy can be considered "safe," regardless of what media/methods you use. You can store "backup" files on floppies or IOmega cartridges, but I've found both of these unreliable for other than short term storage. And I've got several Word docs now crowding 80 MB each, so floppies are useless. (Mickey says don't go past 32 MB for a Word document, but what do they know?)
Windows has built in "backup" utilities, but they require that you have someplace for them to put the backup data. Obviously putting it in another place on a drive that's failing doesn't do much good, so you still need CDs, DVDs, a tape deck, or a separate Hard Drive.