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 many layers of image and sound, colour correct images and mix your sound too for final viewing. Usually, the less you paid for your program the fewer options you get. However, once you get onto semi-professional and professional programs like Adobe Premiere, Final Cut or Avid, you really need to learn the manuals to benefit from it’s attributes- 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, you get good results quickly, and they're not too limiting. Once you've learnt this program, it will be easier to move onto a more advanced program if you want to.
advanced
Simple programs 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 different transitions, better effects and more layers for sound. The time has come to invest in a more advanced program: Final Cut (Mac only), Adobe Premiere (PC) or Avid Media Composer (Mac and PC). These all have very competitive rates for educational institutions, but you will probably need to upgrade your hardware.
All have 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.