In this example, we will install drush under the directory /usr/local/share/. The path is not really important as long as you adjust the following commands accordingly.
If the directories do not exists, we create them:
sudo mkdir /usr/local/share/
sudo mkdir /usr/local/bin/
And now it time to download and extract drush. Make sure that you have the latest version available and replace the url in the command accordingly.
We also create a symlink so that we can use it everywhere without typing the parent path all the time...