To install vim on Debian simply become the root user and type this at the command line:
bash# apt-get install vim vim-rt
The package vim contains the executable, and the vim-rt package contains all the files necessary to get syntax highlighting to work.
If you want to install the graphical version of vim install the packages vim-gtk and vim-rt.
If you're going to be doing programming, you'll also want to install the package exuberant-ctags.