I live in a small town and have only experienced the big city through hotels and tourist attractions so I'm lacking in this area. I know people in big cities have apartments above shops, restaurants and bars etc. but my question is, how do they get up to them? Is there a separate elevator or staircase or something like that? Also, where do they park assuming they have a car?
Are you talking about a particular city? There tend to be certain conventions particular to particular cities, though some stuff is obviously generic.
Yes, there are separate entrances, depending on what you're talking about.
There are, mostly in smaller places or smaller buildings, a back or side entrance or staircase or whatever, to the dwelling above the shop/restaurant.
In larger cities, like NY, the shops below buildings may or may not be actually connected to the buildings you see. I mean they are, but they're not in the same way. In some places there may be a store with two floors of housing above. In NY, there may be a block with shops all along the avenue, and, say, three different buildings above, one with an entrance on the avenue, mid-block, one with an entrance on the side street, one on the other side street. They're all sort of technically above the shops, but most of the apartments in the side street-entrance buildings aren't above the shops, just the ones on that side.
Be careful with the car depending on the city. Some cities, very few people have cars. People who do will park on the street or in garages.
Some cities more people do, and there are parking lots and stuff behind stores.