No training as such is required in advance. You will need to learn how to write up the required reports after each shop.
You will follow the instructions provided for each shop. Sometimes you will have to make a purchase within a certain budget, for which you should later be reimbursed. You may be told to go to the shop location within a particular time frame.
You of course do not want to be identified as a mystery shopper. While you will need to create a report on your experience, you should not be taking notes during the shop.
Shops can be done at all kinds of stores, apartment leasing offices and even on cruise ships… although that last is generally reserved for highly experienced mystery shoppers.
Pay can be fairly low for the time involved when you include travel time, especially in the early days. But you can get the better paying shops as you build experience and a reputation with your employer as someone who hands in detailed and accurate reports.
Transportation to get to the shops in your area. A computer and the necessary software to send in your reports. Odds are you won’t need to buy anything new for this job.
Where to Search for Jobs
There are two current mystery shopping scams I know of. The more recent one is where a company sends you a check or money order for a few thousand dollars, and instructions on how to do your mystery shop, cashing the check and sending the money to a designated recipient. You get to keep a few hundred.
The check is fraudulent, and you end up paying the charges.
The other scam happens when sites offer lists of companies that are looking for mystery shoppers. All you have to do is buy it.
However, most of the lists are useless. They may not list legitimate opportunities, or may only list stores that might use a mystery shopper. The above resources are probably better ways to find companies to hire you.