How does a small aircraft like a Cessna fly at night?
Lets attack this from a few different angles. 


  then night hits and its now pitch black with zero visibility?


There is plenty of visibility at night, a clear night is just as nice as a clear day. As a matter of fact when the air cools at night and clouds roll out you can some times see farther than you can during the day. 

Here's me on a VFR approach (Piper Warrior) in to KLNS at about 10pm one night, you can see the runways are lit up nicely and can usually be spotted from 5 - 10 miles out depending on altitude.


Here is us earlier that night heading away from KABE (those lights are Allentown PA)


(photo credit to my girlfriend who was bravely sitting in the back)

As you can see you can still make out the horizon and plently of land marks. While it may be different during the day you can still fly VFR at night. 


  zero visibility?


Zero visibility during the day is the same as zero visibility at night and as mentioned in the comments will require you to fly IFR if you want to fly., 


  How does he not run into mountains and the like?


Not flying into the side of a mountain is a topic of its own. You should check out my answer here to that very question. 

From a more general stand point there are lots of ways to navigate in an aircraft. Here is a solid answer that covers most of them. The only thing that is not really feasible in a small single pilot aircraft if you are solo is celestial navigation although it could be done.