This plugin lets you easily to add a signup form for your MailChimp mailing list.
Where do I get the API key? You can create one from your MailChimp account.
How do I customize the styles of the signup form? The plugin include a mini stylesheet and it is loaded with the plugin. Simple override any styles defined in the stylesheet.
How to add the signup form by shortcode? You can insert the form to any page/post by using shortcode [anywp_mailchimp_form]. You still need to add a widget and specify those settings in the widget, but you can drag-n-drop the widget to Inactive Widget area if you do not want to show the widget in any sidebar.