Beer

American beer, with very few exceptions, varies from the mediocre to the terrible. There are not many types of beer in the US-"light" and "dark" are two terms commonly used.

It is therefore normal to order beer simply by brand name. In a restaurant, in fact, it is quite all right to order "a beer", and they will tell youwhat they have.
It is not necessary, either, to specify quantity when ordering beer. If it comes in bottles or cans, you will get a bottle or can, and if it's "on tap" you will get a glass, unless you order a "pitcher". The latter is very convenient thing to do, since you can then take the jug and glasses to your table and keep filling up without going back to the bar. (It is harder, however, to know how much you have drunk.)
Some beer comes in bottles with tops that look as if they need an opener, but you can, in fact, screw them off by hand-though you have to be very careful not to hurt yourself. It is possible, in some stores and bars,to find a wide selection of beer from all over the world, especially Western Europe and Australia, and it is good fun to experiment with these.

Cocktails

Cocktails and "mixed drinks" are much more popular and rather stronger in the USA than in Europe, and visitors may not be familiar with some of the terminology. "On the rocks", as you probably know, means with ice, while "straight up" or "up" means neat and without ice.
There are hundreds of different cocktails, and there is no space here to list all the different names.

The Hard Stuff

In America "whiskey" means bourbon unless otherwise indicated. Bourbon is a rather oily spiritmade from maize. Rye whiskey is called "rye" and Scotch
whiskey "Scotch".

Wine

In bars wine can often be bought by the glass. Don't be misled by names such as "Chablis" is used to refer to white wine, and "Burgundy" to red-Americans seem never to have heard of white Burgundy.