Before you install drush make sure mamp is running.
On http://drupal.org/project/drush there is a installation command with pear but that doesn't work .... idk why. But on the documentation site is a alternative way to install drush on osx.
First step is to download drush in your home directory like /Users/username/drush or elsewhere. Just remember the path.
Next tell osx where to find drush
nano ~/.bash_profile or nano ~/.profile
Replace the Path /Users/myusername/drush if you install drush elsewhere. Now logout or reload the profile with
source ~/.bash_profile . ./.profile
Or you can just create a symlink.
cd /usr/bin sudo ln -s /Users/myusername/drush/drush
Don't forget to replace the path.
If you got an error after you used a drush command like
"Error: PDO::__construct():  No such file or directory (trying to connect via unix:///var/mysql/mysql.sock)".
You can solve the error with
sudo mkdir /var/mysql sudo ln -s /Applications/MAMP/tmp/mysql/mysql.sock /var/mysql/mysql.sock