Well, yes and no. If a very patient person went out night after night, she could count up all the stars she could see. But if she then looked through a telescope and tried to count again, she would find many more stars, because the telescope would help her see faint stars that she couldn't see with her naked eye. If she got an even bigger telescope, she would see even more stars!
It is possible for astronomers to guess how many stars there are, though. First, we can use physics to make a good guess about how many stars there are in our galaxy (about 100 billion). Then we can make a guess about how many galaxies there are in the visible universe (also about 100 billion). Then we just multiply these numbers together to estimate the number of stars in the visible universe - ten thousand billion billion stars!
With more than a decade of experience as a science writer, Kate Becker has written on a wide variety of science and science policy subjects for web, print, radio, and television, with an emphasis on astronomy and physics. As a researcher for NOVA and NOVA scienceNOW, the nation's premiere science documentary series, Kate investigated everything from human hibernation to invisibility cloaks. She studied physics at Oberlin College and astronomy at Cornell University, and she's had the good fortune to observe with the Arecibo Observatory in Puerto Rico and the Very Large Array in New Mexico, two of the very best places on this pale blue dot of a planet.