How would vehicles travel through the interstellar medium with its such low density? I've heard from a number of different places that the density in the interstellar medium can have an average of 1 atom per centimeter cubed. Perhaps I have a wrong understanding of what 'nothing' is (I am very knew to astronomy/astrophysics), but how would a vehicle, like the Voyager for example, be able to travel through it? 

My (perhaps very flawed) thinking behind this is that if there are so few atoms not in close proximity, there couldn't be any (meaningful) forces interacting between them to provide any sort of way to travel through it.
The answer is in your question.

You said


  there couldn't be any (meaningful) forces interacting between them to provide any sort of way to travel through it.


That's the great thing about outer space. There normally aren't many particles around that could slow down a spacecraft via drag or friction. If you give something a push in outer space - somewhere that unrealistically is free from any gravitational interaction with other objects - it will travel forever. Objects travel through the ISM via Newton's first law - an object in motion tends to stay in motion.