After installing the module you can access the configuration at Stores -> Configuration -> MAGEMONKEY -> MageMonkey.
Select MailChimp option from the previous menu.
In order to get your MailChimp api key you have to click on the "Get API Credentials" button.
Immediately a new pop up window will be shown asking for your MailChimp username and password.
Then just copy the api key (Keep safe) and paste in the "API Key" field of our configuration click on the “Save Config”.
Finally add the Customer Fields Mapping as shown in the picture below, the right column must match the MailChimp Merge Tags.