Upgrading Ruby to 2.1.0 (and above) in Mavericks

Mavericks comes installed with Ruby 2.0.0, so your current version of ruby should be the following (if you haven't touched Ruby since upgrading to Mavericks):

ruby -v
ruby 2.0.0p247 (2013-06-27 revision 41674) [universal.x86_64-darwin13]

I wanted to use RailsInstaller for this because it's seamless, but they don't have an updated install package for the newest version of Ruby and Mac OS X, so I used RVM instead.
Run the following to install RVM and the latest stable version of Ruby:

\curl -L https://get.rvm.io | bash -s stable --ruby

Install the Ruby interpreter:

rvm install 2.1.0 --autolibs=enable

After that's finished installing, run:

source /Users/{your_user_name}/.rvm/scripts/rvm

Run:

ruby -v
ruby 2.1.0p76 (2014-02-24 revision 45161) [x86_64-darwin13.0]

Then run:

rvm use 2.1.0

Or:

rvm 2.1.0

(The commands are equivalent)

To make this the default version of Ruby for future sessions, run:

rvm --default 2.1.0

After this, I had issues getting Rails 4 to work, the following made it possible:

rvm gemset create rails-4.0
rvm 2.1.0@rails-4.0  

The above allows Rails to store gems associated with the particular folder, otherwise, it will try to compile the system version of Rails. After, install Rails 4.0:

gem install rails --version 4.0.0 --no-ri --no-rdoc

Follow the any messages you might get from bundler to update your gems after Rails has finished installing.