There's a bewildering variety of things you can back up onto. There are floppy disks, tapes, removable hard disks, rewritable CD-ROMs - and by the time you read this, probably three or four other options. Here's the important thing: it doesn't matter which type you use.
It's a good idea to have something which you find easy to use. It's a good idea to have something big enough to put a single copy of all your information on one physical thing - one tape, or one CD-ROM. Two at most. But other than that, it doesn't matter which type you use. There's probably someone who understands computers who you trust, even if it's the staff in a particular specialist computer store. Take their advice.
Your backup media (the thing you back up on to) probably comes with software which will ask which files you want to back up, and will copy them onto the backup media for you. If not, ask your friendly specialist for help - there are too many ways to actually do a backup for me to write them all, and they'll change by the time you read it anyway. But in the following section, I'll give you some advice about what you might want to copy.