simple
In the simplest programs, you can't do much more than put your video clips together in a different order and play them back. Usually you can add titles or music.
With better programs, you can work with lots of layers of sound and picture, mix your sound. Usually, the less you paid for your program, the fewer options you get. However, once you get onto semi-professional programs like Premiere or FinalCut, you have so many options you have to be prepared to really learn the program - and this takes time.
As a beginner, it's best starting your group with something like imovie (Macs) or Pinnacle or Movie Maker (PC). They are intuitive to use, and you get good results quickly, and they're not too limiting. And, once you've learnt this program, it will be easier to move onto a more advanced program if you want to.
advanced
Simple programs are simple because they reduce the number of options. This means the computer decides a lot of things behind your back, so to speak. Once you get to a certain level of editing skills, you will find that you want to have more control over what is happening with your film.
If you enjoyed the experience, you will start to hanker for things like better transitions, better effects and most of all, more layers for sound. The time has come to invest in a more advanced program: The best consumer editing software is probably FinalCut (Mac only), followed by Adobe Premiere (PC). Both come with comprehensive manuals and tutorials, but it is also worth taking part in a course to get yourself up to speed. Find one locally, and get tutoring as a group if you can.