Getting your Linux environment set up for RVM is the hardest part of installing RVM itself. If you're unfamiliar with the process of compiling Ruby from source, you can get a little lost. Thankfully, distributions like Ubuntu make things pretty easy.
These instructions are written on Ubuntu. For the most part, they will apply to any Debian or Ubuntu based distribution. For other distributions, the package names may differ, but the same libraries and such need to be installed.