Parking is a cluster. RTD contracted that out to the Central Parking jackwads who've made it such a pain in the ass.
Here's how it works:
If your car is registered within the district (all of Denver, Jefferson, Boulder, and Broomfield counties, and most if not all of Adams and Arapahoe, and the northern edge of Douglas) and you're going to be there less than 24 hours, you just park and get on the train.
If your car is out of district, you park. Then you go to the vending machine, put in your plate number, and pay for however long you're going to be there.
If you're in-district and you're going to park for more than 24 hours, same deal.
After you pay, you're good to go. Your plate number and how long you paid for is stored in the machine. The piece of paper is just a receipt, and doesn't need to be left on your dash.
And then, every now and then, someone from CPS drives around the lot with an automagic plate scanner which reads the plate and compares it to whatever's stored in the machine. If the machine doesn't have a record of you paying, then it automatically decides whether you get a warning or a parking ticket, and prints it out. (They had to do the automatic decision thing, because the CPS people really are that stupid.)