I've got a second hand Nokia Lumia 820 that I want to use for testing, but I can't figure out how to get my SIM card into it?
You can download the user guide as a PDF. On page 7 of the linked guide you can see how to change the SIM card. Nokia suggests prying open the shell by putting your thumbnail in the seam between the screen frame and the back cover, then bending the cover until it opens. A blunt knife might be helpful if you have troubles prying it open with your fingers.