Q: How can I sync a .mov file of a home-made video?

See:

iTunes: May be unable to transfer videos to iPhone, iPad, or iPod

iTunes: Frequently asked questions about viewing and syncing videos

You may need a third-party program . I use HandBrake, it is free and has presets for the iPad.

Another way. You can use a USB flash drive & the camera connection kit.

Plug the USB flash drive into your computer & create a new folder titled DCIM. Then put your movie/photo files into the folder. The files must have a filename with exactly 8 characters long (no spaces) plus the file extension (i.e., my-movie.mov; DSCN0164.jpg).

Now plug the flash drive into the iPad using the camera connection kit. Open the Photos app, the movie/photo files should appear & you can import. (You can not export using the camera connection kit.)

Secrets of the iPad Camera Connection Kit

http://howto.cnet.com/8301-11310_39-57401068-285/secrets-of-the-ipad-camera-conn ection-kit/

 Cheers, Tom