It all depends on what your Handycam and computer have for connections, and also on your software.
I have a Sony Handycam model DCR-TRV460. It records digital video onto 8mm tape cartridges. At its front edge on the right hand side is a cover over 3 ports. The top round one is marked A/V. t accepts a cable that came with the camera with a 3.5 mm tip-ring-ring-sleeve connector on one end and RCA connectors on the other for Video, Left Audio and Right Audio. This is the analog NTSC composite video signal output, and it can be fed into any computer video capture card for that signal type. Then you just need software to capture that signal as a digital file on your hard drive. (You also can feed signals into the camera using this port, and record them on the camera's digital tape if you wish.)
On my camera, right below that is a small rectangular hole marked DV for Digital Video. It actually is the mini 4-pin version of an IEEE 1394a (aka Firewire 400) port, although Sony tends to call them i.Link ports in their manuals. This will allow Firewire communication both directions between your computer and the camera if you get the correct Firewire cord, AND if your computer has a Firewire port in it. Again, some software is needed to capture camera video to a hard drive file. In my case, this interface is the better option. After all, the data it records on its tape is a fully digitized video and audio, and that data stream can be copied into the computer with no further alteration.
The third port on my camera has a symbol beside it to indicate it is a USB port. The camera can send streaming video out the USB port, but because its data rate is much lower the video quality is not as good.
To do this you should read the manual for your p[articular camera carefully, and see exactly what ports it has. You also have to use the camera's menus to set certain options for this kind of work. Then match up with ports on your computer. My camera actually came with two manuals - the second deals specifically with details of using it with a computer. In fact, one of the fascinating things it tells me is that the camera itself can act as a video capture device for analog NTSC Composite Video from a VCR. Its own analog-to-digital capture chip is always functioning. So I can connect a composite video signal from the VCR to the analog input of the camera, and then connect the Firewire cable from the camera to the computer. If I then set the camera to record the signal coming to it from the VCR, it also forwards the DIGITAL version of that signal out of the Firewire port into the computer for capture there.