Well apart from mapping the stellar distributions locally to get an idea of depth & feature of nearby arms the key way to get an overall idea if our galaxies shape is via radio observations if the neutral hydrogen emission line.

This emission line from hydrogen at a wavelength if 21cm can be plotted across the sky with variances in the frequency denoting relative velocity. combining this with models of the orbital velocity of matter in our galaxies helps in ascribing the emission to actual hydrogen clouds across the galaxy & thus builds up an overall map of matter distribution.