Welcome to the forum. jennie.
Spend a lot of time reading. This section, New Mystery Shoppers, has a lot of information that will help you understand how this works. Being a mystery shopper means running your own small business, working as a contractor to multiple mystery shopping companies.
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.
How much time and effort you put into planning and implementing your business, and how many companies you register with, will determine how successful you are.
Good luck and happy shopping!