In the Northern Hemisphere, only one galaxy is observable
with the naked eye. Messier 31:
The study of distant galaxies has come about because of LARGE telescopes. Around 1920, Edwin Hubble (for whom the Hubble Space Telescope is named after) began looking closely at the great ``spiral nebulae''.
He found Cepheids in M31! He was able to estimate distances.
Recall, Cepheids are stars showing a periodic variation in their brightness, the period of the light variation being related to their absolute luminosity. This showed M31 to be WAY WAY WAY far away, and outside of our own Galaxy.