The main method for counting stars isnt actually counting. It is estimating the stars based off of total mass. We know the mass of the sun = 1 solar mass. We calculate the total mass of the galaxy to be about 400 billion solar masses. Some people equate 400 billion solar masses to 400 billion stars. This is unlikely to be true simply because there are stars several times larger than the sun, and stars significantly smaller than the sun. So if you take that into consideration, it probably is somewhere in the 250billion range. But some people say the stars smaller and the stars larger balance out to be 400 billion stars.
No one can give a definitive answer with the capability we have now. Thats why its important to get the 3rd generation of telescopes and probes into space, starting with James Webb, to replace Gen. 2 Hubble.