Firstly, see if your computer has a graphics card(a simple TV Tuner/capture card will suffice). Secondly, see if the handycam has a S-Video Port. If yes, then you need to buy a S-Video cable. Connect the cable to the graphics card slot.
Run Windows Movie Maker v2.0 and capture the video from handicam. You should have sufficient space ( 20+ GB) in the HDD partision you would store the captured file. Save the captured file (MPEG4 format) in the HDD.
Run Nero and convert the captured file to VCD/SVCD format and write to a blank CD.
Addendum : Prior to start capturing, you should connect an audio cable from handycam to the sound card of your computer to capture the audio.
Hope you succeed in the project.