It is actually a rather complicated deductive exercise using lots of data in radio astronomy and other fields. We know the Milky Way is a very flat system in 3-dimensions, because from the inside, its projection on the sky is a very narrow band of faint stars. We also know it does not have a gigantic nucleus because when we look along the Milky Way on the sky, we do not see a 'ball' of light peeking up from the Milky Way. Using our knowledge of the shapes of other galaxies, we easily conclude it must be a version of a spiral-type galaxy with an unremarkable central nucleus. Detailed studies of the motions of interstellar gas clouds fills in this picture considerably by letting us plot the locations and speeds of these clouds, and in most versions of these studies, a distinct spiral pattern emerges. There is some dispute over exactly where the spiral arms are located, and their pitch angles, but the essential details support the idea we live in a 'late-type' dusty spiral with perhaps a weak bar-like feature in its core.