I did my first shop in the early-mid 1990s for Consumer Impressions after my mom by chance met a person who worked there and explained what they did, she told me so I called and signed up. They snail mailed a package of shops to be done for the next month. To change a date I think you just had to call, which was never an issue. The packages were mailed with return envelopes.
I haven't shopped for them since I moved out of the Dallas area in 1998, but I then did shops for Beyond Hello, Bare Int., and some others that in all honestly couldn't tell you how I found most of them (I think a scheduler at one of them knew someone at Consumer Impressions and they called me). I switched jobs in 2003 and cut way back on mystery shopping for a while. I picked back up again about a year ago.