Updating your repository.

$ sudo apt-get update

Installing ruby, mysql, sqlite and build-essential

$ sudo apt-get install ruby ri rdoc build-essential
$ sudo apt-get install mysql-server mysql-client libmysql-ruby
$ sudo apt-get install libsqlite3-0 libsqlite3-dev libsqlite-ruby

Installing gem package

$ sudo apt-get install gem

Installing ruby on rails

$ sudo gem install rails --include-dependencies

Installing a few useful ruby gems:

$ sudo gem install mongrel
$ sudo gem install capistrano 
$ sudo gem install ruby-debug
$ sudo gem install image_science
$ sudo gem install rmagick
$ sudo gem install RedCloth

Now you may create your first rails app:

$ rails myapp

If you want to use mysql instead of sqlite in your app:

$ rails myapp -d mysql

Resources:

• Installing Ruby on Rails and Ruby on different systems