Using Universal Email and CSS Form Builder
One of the more straightforward ways to implement this would be to use Universal Email first to create the email functionality.
For guidance on using Universal Email, start with the Getting Started Guide found here: universal-email/
Once you have the email functionality applied to your page, use CSS Form Builder to customize the Universal Email page to contain the form fields you desire and look as you would like. Check out the Modifying an existing form with CSS Form Builder How to here: