Astronomers measure the brightness of stars in Magnitudes.
In a fairly dark suburb on an average night, the faintest star you can see is about Magnitude 5.5. There are about 2,800 stars visible down to a brightness of Magnitude 5.5. Of course, these stars surround the entire globe of the Earth, so you'll be able to see only about half of these stars above your local horizon at any given time - say about 1,400 stars. Also, the number of stars you can see depends on your location. For example, in Australia, we can always see the Southern Cross, while people on the other side of the equator can see the Southern Cross only at certain times of the year, and then, only for a few hours.