If you don't mind parting with a bit of money you can turn that hard drive into an external hard drive by getting yourself a USB/FireWire caddy. Something similar to this would be ideal.
If you'd rather have a go at saving your money we can check to see if the older drive will be compatible with your newer system. You will likely need a Phillips head and flat head screwdriver to check and fit it if it looks good.
1. Is your old hard drive IDE or SATA? Click the words to compare
2. Remove (usually the right hand when the computer is facing away from you) the side panel from the computer and take a peep inside at the motherboard. Do you have SATA connectors, IDE connectors or a combination of both?
If you go with the caddy/enclosure option, it's a simple matter of putting the hard drive in and connecting it up to the USB port of the computer.
If you want to see if you can fit it, please answer the questions above Questions of your own you are also free to ask.