Homebrew is a package manager. It's a easy and flexible way to install UNIX tools Apple didn't include with OS X.
If you haven't installed homebrew yet follow the installation instruction for homebrew.
Preparing for drush
After successful installation of homebrew we need to be capable to grab drush from git.
brew install git
This will install homebrew in your /usr/local folder, install git and link homebrew to its git repository.
Using Homebrew you can install Drush install in one command
brew install drush
This will also install Drush Make.
After that you can start running drush on your installation.