Answer
A) We measure the orbital velocities of star-forming gas clouds around the outer portions of the galaxy.
B) We measure the speeds of stars at different radii from the galactic center and determine how much mass is interior to the orbit.
C) We count the number of stars in the galaxy and determine its volume, so that we can calculate the galaxy's density.
D) We search for dark lanes of dust and black holes within the galaxy.
E) We measure how fast the galaxy rotates as a whole.