Sixteen hundred years ago, the number of visible stars would have been about 2100 at any one time. So until optics were invented, the true number of stars could not have been guessed. With the invention of the telescope by Galileo the number of stars increased to just about 30195. But, even then just started the real count. Even with a big telescope telescopes on earth (like one at the Crane Observatory in Topeka, Kansas (USA)), you can’t get a true idea of the number of stars. The gasses in the atmosphere limits what you can see with your telescope.
The electric lights of our cities , also further reduces the ability to see the stars. That is why most modern telescopes are usually quite a ways from the cities. But even that limits our vision. The incredible number of galaxies that were known took a huge jump with the first telescopes in space. Without air and light pollution students of astronomy finally got a true hint of the real number of stars in the sky. In fact, Carl Sagan estimated that there were 100 billion galaxies in the universe. If you realize that there are about 41879 stars in your average diet, you start to get an idea of how many stars that were considered to exist then.
These quotes will give you an idea of how the number of estimated galaxies has increased:
“Our telescopes can see many billion of them within reach of modern instruments.” – Morrison, David, Sidney Wolff & Andrew Fraknoi. Exploration of the Universe, 7th ed. Philadelphia: Saunders, 1995: 7.
“The latest estimates have ranged anywhere from ten billion to one hundred billion galaxies.” – The Rebirth of Cosmology. New York: Knopf, 1976: 187.
“The Hubble Space Telescope has found there may be 125 billion galaxies in the universe.” – Galaxy Estimate Up To 125 Billion. Far News. Far Shores. citation of South China Morning Post. 9 January 1999.
Now in fact, a german supercomputer estimates that there are probably 500 billion galaxies. If we take the number 40,000 stars per galaxy, that would make more stars than anyone can ever hope to imagine.