Here's a link to the Handbrake "user's guide". It's still kind of technical, but if you use the presets in Handbrake, you can't go wrong.
http://trac.handbrake.fr/wiki/HandBrakeGuide
Here's the simplified process:
1. Install VLC (from
http://videolan.org/). It's free.
2. Install Handbrake (from
http://handbrake.fr/). It's free too!
3. Insert a DVD; close the DVD player application.
4. Launch Handbrake.
5. Choose the DVD when the "Open" window appears.
6. Choose a preset on the right side for what format you want (e.g., iPhone, iPad, AppleTV).
7. By default, the file will save to your Desktop. That's good for now.
8. Click Start. The process will take some time, even with a fast Mac.
9. When it's done, it dings. You will now have a file on your Desktop.
10. Launch iTunes.
11. Drag the file from the Desktop into iTunes.
12. Sync your iPhone/iPad with iTunes and enable "Sync Movies".