Start with the threads marked 'sticky' at the top of the New Mystery Shopper section of the forum. There are, however, things you need to be aware of before you decide to go down this road.
1) Many shops will not allow you to take along small children because they want you focused on the customer service you are receiving and a child can be distracting to doing timings, etc.
2) Shops generally pay in the area of $8-$15, so figure out how many shops you will be needing to do per month to supply a continuing source of income to the family.
3) Depending on where you are located, you may have a lot of competition for jobs so it may be difficult even to land junk jobs (generally $10 and under).
4) Most jobs require you spend some money to be reimbursed. This may be a $1 purchase to get a receipt to prove you were at the right place at the right time or, as a $10 fee job I saw today in my email, you may need to lay out up to $50 for a service very likely to be of no use to you and then wait for a month or more to be reimbursed.
So with this in mind, read on. There are 'legitimate' companies out there that are not scams, but there is an awful lot of below minimum wage work (which you can get away with when you hire Independent Contractors--which is what shoppers are).