Welcome to the Mac platform, use Time Machine, connect your external hard drive then open the Time Machine preference in your system preferences. See this link for more information, http://support.apple.com/kb/HT1427
Well there three common methods
1: TimeMachine which Apple provides if you hook up a new external drive it will copy everything on your computer. This is for newbies and allows some animated ability to go back in time to various states of your files and allows you to restore from.
Drawbacks of TM is it's not hold the option key bootable, so if your internal drive dies, you got a dead computer on your hands. It also needs other things to work for it to restore from. Like optical disks, optical drive, internal drives, etc.
2: Carbon Copy Cloner (first free and the best) and Superduper (free clones, rest is payware) which can clone your entire OS X partition and make it hold the option key bootable. This is essential to getting your computer up and operating as fast as possible Scheduling ability in both. All you need is a working port, USB or Firewire, files can be accessed form any computer that can read the standard Mac OS X Extended format.
3: Manual drag and drop copy methods, when you need to free up space or move files, or want a permanent backup or some other more specific use and not a whole drive copy.
4: TimeCapsule and other gimmicks, sort of a TimeMachine + wireless backup system, I don't know as I don't trust wireless to be all that reliable as it's subjective to too much interference from third party sources.
In your case, I would get two external drives equal or larger than the size of your boot drive.
Hook up one drive and let TimeMachine do it's business. It will backup you up and save your data.
Second drive, you need to learn how to use Apple's Disk Utility to format it OS X Extended Journaled with a GUID Partition Map
Then download the free Carbon Copy Cloner and learn how to use it.
Once you come up to speed, then set up the cloning options. Hold option and boot from the clone.
Your computer isn't going to die right away, but eventually the hard drive could fail or you start messing around with it and suddenly it will not boot, that's when TimeMachine is going to fail you and the clone will save you. The clone will allow you to get online and get help.