Your local MVA page may have a "How-to" for buying and selling that explains things. Here is the Maryland one
. A little obtuse. I suppose all the info is there. I'm pretty sure you'll have some grace period between the purchase date and getting the vehicle registered under your name - maybe 30 days - but you probably have to get a temporary registration and paper license plates to put in the windshield during that time.
The main thing is you have to be insured to drive that vehicle, and like the others have said, once you pay and the company confirms, you are insured even if you haven't had a chance to print or receive your card. In a pinch you could drive home in the car without that insurance card even though this is illegal, but carry the sale transaction info and the name and phone number of the insurance company and your policy number. If you are stopped by the police they can call the insurance company to confirm it. They'll likely do this even if you have the card because its possible to have the card without having paid (and thus be uninusred). Most companies send you the card when they bill you in advance, so you could have the card and never pay the bill. Most police will understand if you have the bill of sale showing today's date on it and explain that you just bought it as long as you are in-fact insured. Of course if you've been stopped its for some other reason and you're probably getting a ticket anyways :) Best to print the insurance card before you drive it.
So to drive the vehicle it has to have valid registration and tags, and *you* personally have to be insured to drive it.
Probably in this order:
1) buy the car - transfer title
2) you or seller notify MVA of the sale
3) get an insurance policy for yourself
3a) get temporary registration - seller keeps old plates and returns them to MVA
4) Bring insurance card and temporary tags to pick up car. drive the car home
5) go through the registration process to permanently register the car under your name and get permanent plates