Dee Shops has certainly hit the basics. More specifically, when you sign up with a company you are agreeing to the terms of the ICA which Dee has mentioned. When you request or self-assign a job, you are agreeing to follow the instructions for that particular job.
There is no job-by-job signed contract. And even with the job there may be two sets of instructions--one general set and one specifically for the location/time you are performing the job. If there are conflicts in sets of instructions/agreements, generally the location/time specifics set has priority over the others, but watch in the company's guidelines and if in doubt about conflicts, clarify it with your scheduler or with the company before you do the visit.
As a self-employed person, you are running a business. You need to do your own record keeping for your 'company' that needs to cover what every business covers. You need your records to be good enough that you can determine what you are owed, what you were paid for, what your business expenses are, etc.
The independent contractor has both a down side and an up side. The down side is that it is not consistent employment, you will spend a lot of time lining up work to do, you will occasionally run into unreasonable companies or schedulers, you will occasionally not get paid. The 'not get paid' is a very disturbing situation, but it happens. Sometimes it is nitpicking nonsense, sometimes it is outright fraud when a company 'hires' shoppers when they do not have the cash flow to pay them and sometimes it is due to mistakes you made while doing a shop. The up side is that you have your own business to choose what works for you. There is a great deal of variety in this work. I do some telephone shops, but mostly service evaluations at banks, stores, gas stations, hotels and restaurants. Each job has its own 'personality'. Each company you work with has its own 'personality'.