It is possible, but it involves copying your video (presumably VHS) from one VCR machine to another with a simple sound mixer attched in the middle. Connect a microphone and CD player for the music to the the mixer, and as you copy yout tape, you can add your voice and music.
It's a very outdated way of doing things. And I really would recommend doing it via your computer, with a simple editing package.
Check if your Camera/VCR has an "audio dub" button. If so, you can insert new audio over the tape. Usually it overwrites the original sound though, so be sure that you dont need it anymore.