rvm has a really nice installer.
First, install curl .
Then you need to install the dependencies:
sudo apt-get install build-essential openssl libreadline6 libreadline6-dev curl git-core zlib1g zlib1g-dev libssl-dev libyaml-dev libsqlite3-dev sqlite3 libxml2-dev libxslt-dev autoconf libc6-dev ncurses-dev automake libtool bison subversion libpq-dev
Now, you can use the automated installer:
curl -L https://get.rvm.io | bash -s stable --ruby
After that, log out and then log back in, and you're all set!
ruby -v should return something like:
ruby 1.9.3p194 (2012-04-20 revision 35410) [x86_64-linux]
If it doesn't, then you should look at the troubleshooting page for RVM.