In order to send email via a HTML form, you will need to include some PHP code. And although it may sound easy, it may be a bit more complicated depending on your web host provider. They may have some connection requirements to their email server.
Below is a link on how to build a form similar to what you're asking for, complete with the HTML and the PHP code. You may also want to contact your web host to see if they can assist you. (Just FYI, once you include the PHP code you may need to rename the file from .html to .php).