There's a very large variety of different ways of achieving this and as ever, the ideal solution for you depends on how much you want to spend, how critical your data is and what you feel most comfortable using as a solution.
The simplest solution for less critical data would be to simply put in a second hard drive, acquire some fairly robust backup software (Retrospect is highly regarded) and setup a scheduled backup program to your second hard drive. Should the first hard drive critically fail, you can simply slot in a new one and recover your data from the second drive.
That solution won't of course help you should someone steal your computer or some other disaster affect your home and consequently your computer. That's why you need to decide on just how critical your data is.
To get round that problem you need some form of removable media to store your data on. You can still implement the above, but include a removable USB stick of 2Gb or so capacity and every week or every month schedule a back up to your USB stick and keep that separate from the computer. The size of stick (or other removable media) will depend largely on how much data you store. The first backup with basically just snapshot your hard drive, subsequent backups will incrementally (if you set it to incremental backup) add any changed or additional files to your backup set, but it won't remove any old ones, so you can see how the backup will expand in size. You could obviate this by setting a full backup every month, but that basically just wipes the old one and adds the new one. Any very old files will be deleted and it will take longer to perform, depending on the amount of data you're backing up.
The expenditure on this would be an additional hard drive (which you say you have already), some Retrospect software (can be had cheaply off ebay I'd think) and a standard USB stick.
Or if you're feeling wealthy, get a SonnetTech RAID card, 3 identical hard drives and stripe it to a RAID 6, if one fails, just pull it out, shove in the spare one, rebuild the the array and carry on! That of course won't help you much should an aeroplane crash into your house, but RAID arrays are way cool!