I'll start -
Although I picked up a Model S and not a Model 3, delivery experience should be mostly the same.
I picked up my Model S on December 18th from the International Center. There was a big push for deliveries that month so just like now, they rented Hall 6.
I arrived on time and was greeted and asked to wait in the seating area. They had juice plus water and coffee (Nespresso Machine) in Tesla branded cups.
After about 5 minutes, a rep came to me and asked me to come with him to get all the paper work signed. It was just a table in the lobby. The table had a "Certificate" on it that said Congratulations and my name.
While I was signing the papers, someone else came by and grabbed my keys for my trade in and went to check it to make sure it was all good. They came back and confirmed it was all good within about 5 minutes as well as handed me my old license plates.
After I finished signing the paper work, the rep took me into the main hall where a bunch of Model S were parked. Mine was there with the lights on and waiting for me. I took some pictures in front of it and then the Rep and I walked around the car to make sure everything was good. We did a full walk through of the exterior and interior including how to charge the car and a quick demo of the screen and how everything works. This took about 20 - 30 minutes total.
Once that was done, the rep asked me to wait in the lobby while they brought the car around to the front. Once it arrived in the front, I was handed the keys and that was it.
During the time of pickup, there were 2 other families there picking up their cars.
I believe with the amount of Model 3's that need to be delivered, your experience will be almost exactly the same as mine. Quick and to the point.
Let me know if you have any other questions.