To record with a camera that doesn't have built in recording ability, you can hook up a VCR or DVD recorder directly to it to get DVDs or VHS tapes (ancient!), or you can get an analog to digital converter and record directly to a file on your computer. There is more information about a/d converters in this thread:
viewtopic.php?f=4&t=76
And one more:
viewtopic.php?f=4&t=406
You can film your monitor, as long as it's an LCD, LED, or Plasma display, but you will obviously have problems with glare off of the screen, and also alignment of the camera.