How many stars are in the sky at night?

It depends how good you are at looking for them. If you look up into the night sky from a city, with air pollution and light pollution, maybe a few dozen. If you go into the countryside and wait about 20 minutes for your eyes to get accustomed to the dark (with no streetlights of course), significantly more. If you have binoculars or a telescope, even more. There are roughly 100,000,000,000 stars in this galaxy alone. There is currently no way to know exactly the number of stars in the universe, but the range of 1022 to 1024 is normally quoted in current estimatations.