Being a mystery shopper means running your own small business, working as a contractor to multiple mystery shopping companies. They will not seek you out. You must seek them out.
You need to register with each company, providing your SS# and personal information. Some want you to take tests and you may be asked to provide writing samples. After being accepted to by a company, you will be able to log into their website and look for assignments in your area. Some companies allow you to self-assign the assignments. Other companies allow you to apply for each assignment and the scheduler notifies you if the assignment is assigned to you.
There is a lot of competition in most areas. My advice is to register with as many companies as possible - many of us here on the forum are registered with 150+ - and spend a lot of time reading and researching so you figure out how mystery shopping works and know how to set up your business. It's very time-consuming to get started. Don't get discouraged.
Good luck and happy shopping!