Become a MacRumors Supporter for $50/year with no ads, ability to filter front page stories, and private forums.
Quick reference for getting your Nano video clips to your computer:

If you're a Mac user, then open iPhoto instead of iTunes when you attach your nano; iPhoto will recognize the video files and import them into Events.

On the PC side, it's a little more cumbersome. You'll have to enable disk mode, which is done in iTunes. Launch it and attach your nano to the PC via USB. The nano's settings page will appear, with the General tab showing. One of the General tab's checkbox settings is "Enable disk mode". Check it. Windows will assign a drive letter to it.

Then, using Windows Explorer or My Computer, search in that drive letter's directory for files with a .MP4 extension. You should find all video clips recorded the same day in the same directory. Copy those to your PC and edit as you normally would; they're standard MPEG-4 files, no encryption.

As for getting a DVD onto your nano, grapejucy has already given a solid suggestion: HandBrake. It'll handle your self-made home-movie DVDs with no problem. Copyrighted DVDs take an extra step or two.
 
Register on MacRumors! This sidebar will go away, and you'll see fewer ads.