Unless you've got a SuperDrive in your G5, then you'll have to buy a DVD-burner (it's worth the money IMHO). Different applications can be used to burn DVDs: my own burner came with the Toast-Lite (by Roxio) burning soft which allows me to burn DVDs. Burning data DVDs (you put any kind of file in it, even video and stuff, but it is only playable/viewable in your Mac) is simple enough and I think (I'm not too sure though) that you don't even need a burning software for it: like burning data and mp3 CDs with the Finder's drag-and-drop function, I would suppose that just inserting a DVD-R in your DVD burner/Super-Drive and dragging into it the files that you want burned the dragging the DVD icon onto the trash (should be changed by the burning icon, duh) would be sufficient.
If, on the other hand you want to make a movie DVD playable by any DVD player then a burning soft is indispensable as it will convert the video files you thow at it into the adequate format. It will also create a simple DVD menu.
As for combining the different segments of a movie, then movie editing software is the thing for you. I thought that iMovie and iDVD would be enough to do the job, but as it turns out, you can't add movies into iMovie unless they were shot by you (unless I'm missing something).
Anyway, just open Safari and run a Google search for video editing software for OSX and you should have at least a couple of valid results.

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iMac G4 OSX 10.3.9
RAM 256MB
LW 4.10.5 Basic
ADSL anything from 3 to 8Mbps/around 1024kbps

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