For PS1 games, I use PsxMC to rip the fmvs and audio. The program's available at
this site. It's partially in Japanese but most of the options are easy to understand. You could also try out PSXPlay and the PSXdeAvi patch if PsxMC doesn't work for you (personally, the PSXPlay ripper doesn't work for me). They're all found at the web site I mentioned above.
As for PS2 ripping, you could use something called
PSSPlex if you have a dvd-rom drive. PSSPlex finds .pss files (video files in PS2 discs), and then you gotta use DVD2AVI or something to convert them to avi or mpeg for editing. More info about this program can be found in
this thread. I haven't used this program before cuz I don't own a PS2, so I can't really recommend this method. If it fails, you'll have to capture ur PS2 footage using a capture card and a vcr.