Each dealer will be different.
Go there with another driver. You probably will be taking an additional car back with you
Do a once-over outside in the sun (if it's out).
Take a test drive. Go for five or six miles so the engine oil shows a temp increase.
Sign a bunch of paperwork.
They'll push the extended warranty plans and tire/wheel damage insurance. Tires are the only thing not covered by the 4-year/50k maintenance. If you have serious potholes to worry about, you might consider that wheel insurance.
They will have a recyclable bag of goodies for you. Coffee cup, key chain (I never understood the keychain) and assorted what-nots.
Should have a full tank of gas.
They may toss in floor mats if you didn't order them already.
Go home. Drop off the other vehicle. Take your transport person for a nice, long drive.
Take pictures. Post 'em here after you get back.