The human eye can see about 5000 - 6000 stars in the northern and southern hemispheres combined, but the entire Milky Way has perhaps a few trillion stars in it, but is probably on the large-size for most galaxies in the universe. Based on the Hubble Deep Field survey which looked at very faint galaxies in an area of the sky only a few arc minutes square, across the entire sky there are probably something like 100 billion galaxies in the visible universe so that means there could be ( 5 trillion) x ( 100 billion) = 5000 billion trillion stars in the part of the universe we can see.
Copyright 1997 Dr. Sten Odenwald
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