if you filled in the information when you signed up at mandrill it should be working.
Mandrill Settings
Your Mandrill Account Username
API Key
Once you have signed up for a Mandrill account, you can create an API key in the Mandrill Web Application.
Use Mandrill for all emails? Yes
If enabled, all emails sent from your community will use Mandrill's SMTP server. Otherwise, only bulk mails will be sent using Mandrill.
Create a test account with a test email address like yahoo or google and see if yo get it.