Have your /etc/apt/sources.list file configured properly with the proper repositories. There is no candidate for Avidemux in the official Debian repositories, but Christian Marillat Nerim Unofficial repository should have packages for you.
Refer to this website for getting the right repository addresses and options to add to your list: http://hpisi.nerim.net/ (sometimes the url changes, so it is a good idea to track http://www.debian-multimedia.org/).
After you have added the appropriate lines to your source file, do from the console (or via whatever GUI program you have for accessing apt with):
apt-get update apt-get install avidemux
This should install Avidemux on your system if just about the most painless and easy way possible. To start Avidemux, in general the command is either 'avidemux' or 'avidemux2'.