To use Time Machine, you have to format it in "Mac OS Extended (Journaled)". Use Disk Utility > http://pondini.org/OSX/DU1.html Copy your files on your external disk to the internal one before formatting the external drive.
Then, open System Preferences > Time Machine > Select Disk, and choose your external drive. The first backup will start, and Time Machine will make automatic, hourly backups. See > http://support.apple.com/kb/HT1427
If you don't like Time Machine, you can use applications like SuperDuper or Carbon Copy Cloner, or Disk Utility's Restore feature to make backups of the Mac. The advantage of them is that you can start up your Mac from them