Alot depends on what kind of videos you're working with. Virtualdub is great for anything in an AVI wrapper; but that doesn't include MPEG1 or MPEG2 (what's on a DVD or received with a TV tuner card), probably in large part because of software patents.
To convert MPEG1/2 to AVI (which confusingly does include MPEG4), you can use
VirtualDubMod. There's a plugin for VirtualDub as well, but I've never gotten the sound to work right.
To edit MPEG1/2 and make another MPEG1/2 file of the same type and picture size, I like
MPG2CUT2. Its interface is a little unusual (its buttons have single key characters, which they correspond to, instead of text), but it can handle more messed-up MPEG files than any other app I know of. Be aware that you can only cut video this way at certain places, at the ends of Groups of Pictures, or
GOPs.
Encoding full MPEG2 is the most difficult thing to find free software for. I don't know of any free software that's easy enough to use for a newbie. You can try
TMPGENC free for 30 days, before it only allows you to encode MPEG1.
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