Most people will not do a computer backup until they learn the lesson of lost information the hard way. I am no exception, I lost a lot of valuable contacts, pictures and files from failing to backup.
To backup up information, you will need some external way or storing the information and files. An external hard drive, or a USB drive are very good methods to backup your computer. Or if you prefere, get a hard drive and a USB hard drive case and make your own computer backup drive.
If you want to be sure your data is 100% safe. Use an online backup service. You can get a couple of gigabytes of backup for free, if it's not enough room, upgrade to an unlimited package for a small monthly fee. An online photo backup is a great idea since this is something you really don't want to lose.
Any time you are backing anything up, don't compress or archive, just do a straight file copy. If a part of the archive becomes damaged your backup is useless.
A good battery backup unit will not only shut down your computer properly for you, if the current to your computer is too high or low, it will also stabilize the power.