Other people are saying to get an enclosure for your hard drive. Since you are not a computer guru, let me explain this to you...

What you want is a "USB hard drive enclosure." Make sure that you get the kind that works on "ATA" and/or "EIDE" drives (two names for the same thing). You do NOT want one for "SATA" (SATA is relatively new, and you said that your computer was old). If your old computer was a desktop system, you want a model that holds 3-1/2 inch drives. If the old computer was a laptop, you probably want a 2-1/2 inch enclosure.

All you do is take apart your old computer, and remove the hard drive (it is a silver box connected to the motherboard by a large ribbon cable). One side of the box wil be silver with stickers on it, the other side will be a circuit board and chips. You remove this drive, and place it into the enclosure. There will be two cables: power and data. Both are keyed so that you cannot plug them in backwards. Four screws will attach the drive to the enclosure.

Next step is to turn on your new computer, and just plug the enclosure into a USB port. Copy your files off, and you are done.

For extra security, you can re-format your old hard drive, and copy all of your precious files to it about once a month. That way, no matter what happens to your computer, you will still have your files backed up.

I hope this helps.