Look up the Sloan digital sky survey. Its work is INCREDIBLE. Also, thanks to such surveys, we know the distances of the stars and whether they're interacting gravitationally, as in following the same orbit around the galactic center, comparing their distance to much closer stars we know are in the galaxy with 100% certainty etc. By measuring the position, trajectories and so on, we can accurately determine its shape. On the Sloan survey website you can load up the 3d map and go fly through the universe, everything you see is exactly how it is out there in the universe