Go the groups page by clicking on Groups in the left-side navigation.
It will take you here:
Click on the group of people whose email addresses you want to download for Mailchimp. Let's choose "Alumni"
Click on the link in the upper right hand corner titled "Export" and click "Download Emails for Mailchimp"
This will download a CSV file ready for you to upload to Mailchimp.
From there, follow these instructions on how to import your list into Mailchimp.