Yes, it is possible. In fact, it's what PHP was designed to do.
First off, since you're new to PHP, I strongly suggest you get to know the
official PHP documentation page, as it will contain all the answers to your questions in some shape or form. If you can't find the answer there, we can help here.
Specifically, you might want to look at the
tutorial found there, as it contains a simple example of how to process forms. Additionally, sending mail is very simple if PHP is setup to do it (you'll probably need to check with your hoster in order to find out if it is or not). Check out the
mail function.