From the top right of your dashboard you can access the component Options.
The options are divided into 2 tabs - "Main Settings" & "Permissions" . The main settings is the area where you need to provide your API keys (we'll discuss that in a second) . Permissions is the place where you would define who is able to access the component in the backend. We use the standard Joomla ACL for that so it is best that you read the documentation available at http://docs.joomla.org .
In order for the component to work you will need to provide your Mailchimp API key. To get the key log into your profile on mailchimp.com . Then on the left click on your name -> Account Settings -> Extras -> API keys -> API keys.
You will be presented with a list a keys similar to this one
Select the Mailchimp key (or if it doesn't exist create one!), copy it and then paste it in the Mailchimp API key in the CMC configuration settings.