About backing up:
If you have a disc burner, you can back up to discs.
If you have another physical hard drive, you can back up to that.
If you have a flash drive (a.k.a. thumb drive) you can back up to that.
If you have anything else (except the original hard drive on which Vista is installed) you can back up to it.
Important note:
Be sure to back up all of your files (but not programs) before repairing or reinstalling Vista. I say don't back up programs because that will be a waste of time: The registry entries that tell the computer that the programs are actually installed will disappear when you reformat the hard drive and/or reinstall Vista. If you keep the installer programs (like me) , though, you can keep those so you don't have to keep downloading them.
About repairing Vista:
If you kept the original Windows Vista Installation disc, you can boot to that. Act like you're going to install Vista, and you should get to a screen that says the install program found this existing installation of Vista and would you like to repair that instead of installing a fresh copy. Try that.
About reinstalling Vista:
If repairing doesn't fix the problems, you'll have to reinstall Vista. Be sure to reformat the hard drive to get rid of the original installation first.