lol at Gator, he is right but only because he took you litterally.
I'm sure you are just wanting to back up your documents and music and such. If you are running XP or Vista, just plug it in. It will/should (depending upon why you are taking it in for repair) display in my computer. You can then just drag and drop your files from you My Documents (assuming you put all your files in there) to the USB drive. If you have multiple profiles (meaning more than one person signs into the computer with their unique ID) you will have to grab the files from each of their My Documents folders.
Do you need to back up your e-mails as well? What do you use as an e-mail client? Outlook? Outlook Express? Something else? If it is web-based Google, Yahoo, Hotmail, you don't need to worry about it, it is stored by Google, etc.