How do I install ruby 2.0.0 correctly on Ubuntu 12.04?

follow below steps

sudo apt-get -y update
sudo apt-get -y install build-essential zlib1g-dev libssl-dev libreadline6-dev libyaml-dev
cd /tmp
wget http://cache.ruby-lang.org/pub/ruby/2.0/ruby-2.0.0-p481.tar.gz
tar -xvzf ruby-2.0.0-p481.tar.gz
cd ruby-2.0.0-p481/
./configure --prefix=/usr/local
make
sudo make install

Use rvm to install stable ruby:

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

or, if you have rvm already, get stable version:

rvm get stable

Install ruby and use the specific version of ruby (remember to use login shell)

/bin/bash --login
rvm install 2.0.0
rvm use 2.0.0
rvm rubygems latest
ruby --version

As found on the official RVM website.

EDIT: As @prem points out run this at first and follow the above steps if there is a public key error

gpg --keyserver hkp://keys.gnupg.net --recv-keys \ 409B6B1796C275462A1703113804BB82D39DC0E3

Use rbenv to install ruby:

Install necessary dependancies:

sudo apt-get update && sudo apt-get install git-core curl zlib1g-dev \
build-essential libssl-dev libreadline-dev libyaml-dev libsqlite3-dev \
sqlite3 libxml2-dev libxslt1-dev libcurl4-openssl-dev \
python-software-properties libffi-dev

Install rbenv:

cd
git clone git://github.com/sstephenson/rbenv.git .rbenv
echo 'export PATH="$HOME/.rbenv/bin:$PATH"' >> ~/.bash_profile
echo 'eval "$(rbenv init -)"' >> ~/.bash_profile

git clone git://github.com/sstephenson/ruby-build.git ~/.rbenv/plugins/ruby-build
echo 'export PATH="$HOME/.rbenv/plugins/ruby-build/bin:$PATH"' >> ~/.bash_profile
source ~/.bash_profile

Install ruby:

rbenv install -v 2.0.0

From the travis-cli installation instructions for Ubuntu, the Brightbox Ruby NG(NextGeneration) ppa:

$ sudo apt-get install python-software-properties
$ sudo apt-add-repository ppa:brightbox/ruby-ng
$ sudo apt-get update
$ sudo apt-get install ruby2.1 ruby-switch
$ sudo ruby-switch --set ruby2.1

Although this answer was accepted, I would strongly recommend using rvm rather. I had nothing but trouble trying to install ruby without it. See e.g. this guide:

https://www.digitalocean.com/community/articles/how-to-install-ruby-on-rails-on-ubuntu-12-04-lts-precise-pangolin-with-rvm