Understanding the hybridization of cyclohexane?
I'm having quite a fair bit of trouble comprehending the hybridization
  of cyclohexane.


Atoms can be hybridized. Not entire molecules. Just atoms. 


  I understand that this is a ringed structure with single C-C bonds,
  therefore all the carbons should have sp3 hybridization right?


Yes, all the carbons in cyclohexane can be said to be sp3 hybridized. 


  I'm reading about how it not planar like benzene is, and adopts a chair/boat conformation which I am having trouble visualizing as well.


In benzene all the carbons are said to be sp2 hybridized because benzene is flat. Carbons which are sp2 are in the same plane with their ligands. Sp3 carbons are not flat with respect to all their ligands. 


  why are the sp3 carbons not planar (not flat)?


You seem to be adept at identifying sp3 carbons. So I won't go over that. 

Within the framework of VSEPR theory - 

1) Atoms are made of charged particles, namely, protons and electrons.

2) Protons are at the core (nucleus); electrons are distributed around the protons.

3) Electrons repel each other (like charges repel). 

So if we have 4 atoms arranged around a central carbon atom the lowest energy conformation or the configuration which will keep each of the 4 atoms the furthest apart is tetrahedral. The angle between the four ligands in a perfect tetrahedron is about 109.5 degrees. If we constrain ourselves to 2 dimensions and force all the atoms to exist in the same plane then the best angle of separation we can achieve is 90 degrees (imagine carbon to be at the center of a square with each corner of the square representing an atom). Clearly, 109 degrees > 90 degrees so the tetrahedral configuration is favored.