When you hit the submit button it will go to process.php. This is defined in the action part of your form. You place the code you want to execute inside process.php.
You are using the POST method. This is how it sends the data from your form to process.php. Post is hidden from the user. Just for the sake of learning if you change POST to GET then you will see the values being submitted in the url after clicking the button.
What is it that your process.php is suppose to do? If it is just to e-mail you through details then that should be simple enough.
I suggest to make sure the form is working you should echo all the values posted in process.php. Then you know for sure that you have the values and can do what you want with them.