How do I record home videos through the computer?

I tried using CamStudio to record the computer screen as I play home videos. I tried playing the DVD through two different media programs, but CamStudio won't record the screens, even though everything else records just fine, so it isn't lag or anything.

Fish out of water? Hmmm!
As they are your own files they won't be DRM protected.
So, rip the files from the DVD to your hard drive, they will be in .BUP .IFO and .VOB format. The .BUP (backup for .IFO) and .IFO are only there to tell your player how to deal with the .VOBs. As they are your own files the .VOBs can be renamed to .MPG and still play and be manipulated/edited by basic video editing programs.
Many video editing programs will accept .VOB files as well as .AVI and .MPG.

But if the files are DRM protected then you need something like AnyDVD to act as a driver between your computer's DVD__CD drive and the computer. I believe that AnyDVD strips off the protection "on-the-fly" and it is illegal to use such software in certain countries, such as the UK. But if you live elsewhere then this is the link:
http://www.slysoft.com/en/anydvd.html

Yeah, you can use something different to help you record video from computer screen. As you mentioned that you want to record video from DVD, then you should use screen recorder to help you.

It can capture any onscreen activities. You just need to play the DVD on your computer, and launch the program, it will help you capture DVD video automatically. You can also convert the recorded video to different video formats.

You can refer to http://www.screenrecord.net/capture-video-from-dvd.html