Get your Mailchimp API Key
Log into your Mailchimp account and then go to this Mailchimp API key link. Alternatively you can go to Account > Extras > API Keys once you are logged.
Configure the Mailchimp Mate Plugin
Go the WordPress Admin on your website. Then, on the left hand side, select Mailchimp Mate > Mailchimp API. Insert your API key into the input box. You can test the validity of your API key with Test Mailchimp API Key. Then you can set it by clicking Update Mailchimp API Key.
Using a PHP Constant
Alternatively, in your WordPress PHP code, you can set the API key with the following code:
define('WPMCMATE_MAILCHIMP_API_KEY', 'YOUR_MAILCHIMP_API_KEY');