how to backup my computer?

If you're going to use Apples Time Machine you need an external disk AT LEAST the same size as your internal hard drive, twice the size is recommended. http://support.apple.com/kb/HT1427 and http://pondini.org/TM/Home.html

If you want to keep a bootable clone of your hard drive get either Super Duper http://www.shirt-pocket.com/SuperDuper/superduperdescription.htmlor Carbon Copy Cloner http://www.bombich.com and an external hard disk at least the same size as your internal disk and follow the directions of the application you choose.