1. Let’s work from your Downloads folder.
    cd ~/Downloads
  2. Download the Ubuntu Fonts package from Ubuntu.
    wget http://font.ubuntu.com/download/ubuntu-font-family-0.80.zip
  3. Extra the downloaded zip file.
    unzip ubuntu-font-family-0.80.zip
  4. Rename the extracted directory. (Not a must)
    mv ubuntu-font-family-0.80 ubuntu-font-family
  5. Copy the extracted directory to the system shared fonts directory.
    su -c 'cp -rv ubuntu-font-family /usr/share/fonts/'
  6. Set the permissions for the directory you just moved.
    su -c 'chmod 755 /usr/share/fonts/ubuntu-font-family'
  7. Scan and build the fonts cache files for the new Ubuntu files.
    cd /usr/share/fonts
    su -c ‘fc-cache ubuntu-font-family’

That’s it, you should now be able to use the Ubuntu fonts in your applications and documents.

Here’s a video of the process.
How To install Ubuntu Fonts on Fedora 16