and from what I understand in one day you can drive and cross 2 or more country borders.
Yep. Imagine driving across the Eastern states. There's been more than one day in my life where I've briefly visited three countries.
How do they all get around if they don't' have cars to drive?
Public transportation is pretty awesome, when well-implemented. A lot of people in Europe have cars, but a lot of them don't. If trains, streetcars, buses, and such suffice to get you where you need to go, why pay for the upkeep of your own vehicle?