If you don't want to open your new computer, play with jumpers, etc., you can buy USB Universal Drive Adapter.
I bought one yesterday for $30.
It's a box, which looks like external HD. You slip your old HD in, connect power, and data cable inside (provided), close the box, plug it in to a power source, connect to your new computer via USB cable (all provided), and your are ready to go.
It'll show up in Windows Explorer as a new drive.