How to install the Pantheon desktop environment?

This is answer for newer releases of Ubuntu — 12.04 and up. Remember, use this at your own risk!

• Open a terminal (Ctrl+Alt+T).

• Add the repositories and update the package list:

   sudo add-apt-repository ppa:elementary-os/daily
   sudo add-apt-repository ppa:elementary-os/os-patches
   sudo apt update
  

• Upgrade your packages...

   sudo apt upgrade
  

• ...and install:

   sudo apt install elementary-desktop
  

After completed installation log out and chose session called Pantheon in LightDM.

1. Open a terminal window (press Ctrl + Alt + T).

2. Run these commands line by line in the terminal:

   bzr branch lp:elementaryos
   cd elementaryos
   sudo sh congrego.sh --configure-installed

3. Logout?Restart and select Pantheon on the login screen.

All answers work but they install the unstable builds, so if you want the stable builds use Ubuntu 12.04:

sudo apt-add-repository ppa:elementary-os/stable
sudo apt-get update && sudo apt-get upgrade
sudo apt-get install elementary-desktop

Now, after you login to Pantheon Desktop it will still look like regular Ubuntu, to easily modify its appearance install Elementary Tweaks:

sudo apt-add-repository ppa:versable/elementary-update
sudo apt-get update && sudo apt-get upgrade
sudo apt-get install elementary-tweaks

The Elementary Tweaks app is an icon at the main System Settings. Change all possible entries to elementary at Appearance tab.

You may want to install more apps from Elementary, but with this you get most of it.