Storing form submission data in a database isn't terribly complicated on a fundamental level. You start by creating a database that has a table with fields that correspond to the form fields. Then your PHP scripts simply gather the form submission data and handles the interaction with the database server to store and retrieve that data as needed. But things do get a bit complicated when you start to consider issues like website security, form data validation, data formats, and a handful of other issues.
I'd suggest that you search for PHP tutorials on forms and MySQL. That will get you started. Once you have the basics down, you can investigate some of these other topics.