If your camera has firewire then use that (you may need to get a firewire card, but they're pretty cheap). If not, then you'll need a suitable capture card for your computer. Some graphics cards have video capture - look for one with "VIVO". Same goes for some TV cards - if they have a phono socket (usually yellow) then they should be able to capture video from your camcorder.
For capturing, there are several programs you could use. Virtualdub's pretty good, and lets you do some post-processing on the video as well. Depending on the system, you'll either be able to use the computer to control the camera (only if connected through firewire), otherwise you'll have to start the capture on the computer and then start the camera playing (and then later trim the first few frames). To capture sound, use the line-in input on your sound card with a suitable adapter, *not* the microphone input. If you're using firewire then that may carry sound as well.