Well, ..., that depends on the following factors:
1) Aperture for the Telescope
2) Focal length of the Telescope
3) Magnification
4) Atmospheric conditions (Seeing, Transparency, and Cloudiness)
5) Phase of the moon (it is a major source of light pollution)
6) Severity of Light pollution
7) Size and Brightness of the Galaxy in question.
8) Proximity to the Zenith.
Given a 6" aperture and 1200mm focal length with a 25mm plossl (48x) in the yellow zone (light pollution) with a clear dark sky with objects near Zenith:
M31 will appear as a very bright fuzzy patch having a bright fuzzy core gradually diminishing in luminosity as your eye travels toward the edge of your field of view. The longer you remaing at the eyepieve the more structure you'll be able to discern.
M51 - will appear as a barely perceptible set of two galaxies. One larger than the other with the larger once having a bright central core brighter than it's edges. The small galaxy will appear uniformly dim.