There seems to be quite some disagreement about the number of stars in our Milky Way, but the most commonly given figure is 100 billion stars. (That's 100x109 or 1011 to be exact)
Other sources put the estimate as low as 4 or as high as 400 billion.
The reason for this inaccuracy is mainly that we cannot see (and therefor cannot count) most of the stars in our galaxy, due to clouds of dark matter, lack of telescopes with high enough resolution and the fact that a far-away galaxy appears the same as a not-so-far-away star. Scientist thus extrapolate the number from what they can see and comparisons with other galaxies that are believed to be similar to our own.
The human eye, btw, can only distinguish several thousand stars on the clear night sky.