What Software Would One Use To Make An Overdub?

I see people on YouTubes making overdubs, and while I doubt they’re strictly legal, some (not all but some) are very funny.

What kind of software does one use to make these? I have a lot of time to kill and would like to try it, if it’s not outrageous.

If anyone has a link to a site that gives a beginner information on how to do it, it’d be great.

[I didn’t know if I should put this in GQ as I wanted fact on software or in CS as it’s kind of an artsy thing. Please move if appropriate]