It was relatively smooth and quick.
There's the paperwork part, which took about 15 minutes and the walk through, which took closer to half an hour. If you already test drove a Tesla, the walk through is pretty much redundant, but they didn't want to skip it to make sure I fully understood everything before driving away.
Given that you're in CT, they'll put a temporary license plate on your back window and you should get your permanent plates shipped to you in about 3 weeks. Emmanuel was my DS, was responsive on the phone and allowed me to pick up earlier than the site originally had showed. Tesla website was very slow to update in comparison. When I was en route to take delivery of my car, my status online still showed "your Model S is in transit to delivery center."