I mean the REAL SOURCE FILES -- these "files" will most likely on a MiniDV TAPE. If you can get and import the masters yourself, that would be ideal because you would be starting with the best copy available before ENCODING it into multiple formats (like to DVD, but also to WMV, MOV, and Flash for the web). Ripping from the DVD can be done, but you're going to have your work cut out for you and you'll be re-encoding lossy on top of lossy -- but it can be done and it can look fine (just more "Tivo'ish" or VideoCD'ish if you know what I mean. Anyway, you're going to have to learn a whole lot of shit before you pull it off.
If you are just going to take "clips" from various DVDs, and not re-edit or make a mash-up of multiple clips, then you might be able to find various ripping apps that can rip straight down into various formats like MPG, WMV, MOV, and FLV. Then just rip down segments into the format you want. Otherwise, you can try editing the MPEG2 in the timeline of your video editor, but most NLEs can't edit MPEG2, and often you run into even more problems because the audio is in a seperate file, so you have to get that into the timeline and synced up before editing it.
Anyway, it can be a PITA for sure and should be avoided at all costs for all sorts of reasons -- some may tell you otherwise, but trust me on this. However, if it is the only source you have, then it is possible. You either have to find an editor that can edit MPEG2 or you have to convert it into a format that your editor can handle first. Then edit it, then re-encode to new formats. Vegas is one app that can edit the MPEG2 natively, but it can't edit the AC3 dolby digital files. So, if you're dvds used PCM audio files (think: wav), Vegas would work, but if those DVDs use dolby digital AC3 audio files, then vegas can only edit the video but not the audio. So, a lot of times, you have to go to an intermediary video codec first, then edit that, and then render out new versions. But that of course adds even one MORE step of lossy compression typically.
One thing also to watch out for is "AVI". All avi is is a "wrapper" or container for video files. It can have a lot of different codecs that all use .avi. So, when you "rip" a DVD with some random freeware app, in all likelihood, it's probably ripping down to XVID or DIVX, which is something you probably don't want to do if you want to edit it at all because most video editors can't edit natively in those codecs either. The exception to that is an avi that uses the DV codec. That's the codec that all MiniDV-based camcorders record at, and it is equivalent to "standard def" TV. The files are HUGE. So, if you can capture to that kind of AVI format from the DVD, then at least you can edit using as good of a copy of the DVD as you can get, and then encode out from there.
Good luck!!!