I've never been a mystery shopper before, but I am thinking of trying it out!
But, before I fill out all of the applications and things I want to know....
What exactly does a mystery shopper have to do?

I get the basic idea of it but I would love some of you to tell me more about it! I would especially like to know what you have to do when you are at a store, restaurant, etc. Since I'm more of a quiet person I'm nervous about having to deal with salespeople.
Any information would be great!

Shops can be simple or complex, require few interactions or a lot of interactions, a few observations or a lot of observations. Lets take a very basic gas station visit. You drive in, put a couple of bucks worth of gas in your tank, check to see that the window washing unit has a squeegee, water and paper towels, then go inside and make a small purchase, checking the courtesy of the crew member, check the restroom for cleanliness and you are on your way. This is the basic theme, but variants can include taking photographs, doing a 'reveal' where you present the associate in the store with a printed notice that they have been shopped and take a lot more photographs. Overall quick and simple. You have collected receipts for your purchases and once home you scan the receipts (or photograph them with your camera), do a fairly simple report, upload the receipt and any photos to the website of the company that hired you and then wait for a month to six weeks to be reimbursed for your small purchases and paid a fee.

A slightly more complicated shop would be at a grocery store where you are interacting with associates in various departments, checking the restroom, making a required purchase or two, counting open registers and the number of customers in the longest lines and noting your arrival and departure times. Again getting a receipt for your purchase and scanning or photographing it to upload with a report.

A casual restaurant is a little more complicated in that you are observing service times, whether the server did specified things, whether management was an active presence and also reporting on the taste, temperature and appeal of what is served you. Those reports frequently pay little if anything, take a while to write up and generally reimburse your meal and tip.

This is not rocket science. Rather it is systematic observation.

Another good example is McDonalds. You go to the drive-thru and when your wheels stop you hit the timing button on your cellphone (or whatever). You order specific items (you've given a choice of about 4 items) and then you hit the timing button again when you pull up to pay. Finally once they've handed you the food you hit it again and you're done with the drive thru. In the restaurant itself, you join the shortest line and hit your timing button. Again you order specific items (choice of about 4) and then you hit that button again when you pay. Once you have your items you hit it for the last time and you go eat. While you're eating you check the cleanliness of the restaurant and how the supplies station is stocked. You go and check to see if the restaurant is clean. You hang around for about 15 minutes and you're done.