To back up the MacBook Air, you have different applications and methods. The most normal in OS X is using Time Machine > http://support.apple.com/kb/HT1427 Time Machine is an automatic backup system that creates automatic, hourly backups of your computer onto an external drive, that will be converted into the Time Machine drive. To set up Time Machine, open System Preferences > Time Machine > Select Disk, choose your external drive and the first backup will start inmediately. If you want to change the backup frequency, you can do it with TimeMachineEditor > http://timesoftware.free.fr/timemachineeditor/
Another method is making clones (simply, copies of your hard drive onto the external drive), using an application like Carbon Copy Cloner or SuperDuper, or just the Disk Utility's Restore feature. The main advantage of this method is that it creates bootable clones, so you can start your Mac from the external drive in case the internal drive is damaged, or to restore the data.
What most users recommend is to make Time Machine backups and clones, but Time Machine should be enough. You have all the differences in this site > http://pondini.org/TM/Clones.html