In the US we're stuck using a dealership system from WWI.
So things aren't always as clear cut.
Essentially:
Drive up to dealership and be set upon by a commissioned salesman within a minute.
There will be some friendly banter and chat about your wants/needs etc.
If you've picked out a car and want to buy, you then haggle the price. In the US cars will have the MSRP (Manufacturer Suggested Retail Price) on the window sticker. Then the dealership may add another sticker with any options/services they added themselves. Dealerships also have what's called the "Invoice" price. Invoice is supposed to be how much the dealership paid for the car from the manufacturer. However, most dealerships get rebates and incentives from the manufacturer so they often pay under Invoice.
There will also be destination charge (delivery from the manufacturer to the dealership, unavoidable), as well as a Documentation and Processing fee (might be argued into the price.) There's also TTL (Tax, Title, and License). These are state fees that can sometimes be argues into the car's price, but usually are kept separate. These fees will vary from state to state.
Be careful, if you're trading in and/or getting financing, the salesman may jump straight to your monthly payment. By doing this, he can play with the numbers to get himself the best deal. ALWAYS keep your numbers separate. New car price, trade-in value, and interest rate. Discuss them individually and don't let them start mixing them together.
Once you've signed, you have to have insurance on the car to drive it off the lot. If you already have an insurance policy you have about 24-48 hours (varies) to talk to your insurance company and insure the new car. If you don't already have a policy most dealerships can get you insurance immediately.
BUt at this point you can drive it off. To sum up:
Pick car
Agree on price
Pay Price, less trade-in, plus Destination, Doc fee, and TTL.
Get insurance if needed
Drive off
The good news is that there are a LOT of dealerships in the US. If one rubs you the wrong way or treats you badly, there's probably another of the same make not far away.
But really, there's no reason why we shouldn't be able to buy direct from Subaru or whatever and have the car dropped off at our homes. But that's an argument for another thread.