Getting files from one hard drive to another

Ok, newb question for y'all. My rather old computer finally gave out, I can't get it to stay turned on for more than ten seconds. Rather than spend forever trying to figure out what's wrong with it I'm just going to go out and buy some pre-made computer somewhere, you know, the kind that come preinstalled with XP and you need to spend an hour or so getting all of the crap off of and the setting right. I just don't have the time at the moment to custom build anything. Now my question is, how do I get the files off of my old harddrive and onto the drive in my new computer? I'm guessing I can't just replace the new one with the old one and expect everything to work properly. Obviously I have to reinstall any programs, but I have several recent files that I never had a chance to back up.

When you get the new computer You can plug the hard drive you have and set it to Slave...

I've never done this so maybe someone who has can tell you more about it..

FYI, if your old computer only stays on for a short period, it's probably a bad power supply. Not that this matters if you're replacing it... but... could be a fairly cheap fix.

If you still buy the new computer, you can set the jumpers on your old drive to make it a slave and just add it to an IDE cable and power it... everything should come up and recognize it and you should be ok to copy stuff over.