The first thing you must do is creating an account on MandrillApp. After creating an account (or logging in to an existing one) you can click on the 'SMTP & API Credentials' link to see your SMTP credentials.

Then click on the 'New API key' button to generate a new key.

Move to your MAMP PRO application and navigate to the postfix configuration (Server - Postfix).

Enter the details from the SMTP credentials page into you postfix configuration. The password can be any valid API key.

That's it!

bonus!

You can go into test mode with Mandrill. This options lets you send mails trough smtp without actually delivering them. No more development-emails to you clients!