Beef Barley's advice is good, and the tutorial he put together is informative, but he is a fan of FixVTS, and if you're having a problem with Shrink and Nero, I think FixVTS is a tool you should consider later, when you get more experience doing this. (It's not really a tool for beginners).
One thing you'll find as you go... a good set of tools is worth its weight in gold... two programs you should add to your toolbox right away are VLC Media Player and Imgburn. They're both available on the web and both are freebies, and both are 'can't-do-withouts'.
Unless your kids favourite movies are films like Bridge On The River Kwai, The Longest Day, Gone with The Wind, etc., compression of a Main Movie only rip to fit on a single layer DVD shouldn't be necessary, thus you won't need DVDShrink.
Nero is OK for burns, I guess, but I prefer Imgburn (as do many here...).
Simply open Imgburn, select write files, point the program to where you saved the DVDFab HD Decrypter rip of the main movie, answer a few prompts (make sure a blank DVD is in your burner), and let Imgburn do the work. When you're comfortable with this burner, there is an option to remove the prompts, and start the burn as soon as the burner knows where the files are.
If you like (or feel the need), VLC media player can be used to check the rip when it's finished by DVDFab (it'll play almost anything) to make sure the rip is OK.