How do substances with like charges repel each other? I have read in a number of places how substances with opposite charges attract each other:
The excess electrons in the one substance repels the electrons in the other substance so that they move away from the surface, leaving the protons closer to the surface which are then attracted to the excess electrons in the one surface.
But I have not found any parallel explanation of what happens when substances with like charges are brought near each other.
I'd also be grateful for an explanation of what happens when two electrically neutral substances are brought near each other.
 A: It seems that the explanation of the attraction assumes we understand the repelling case. Explaining that case on the same level of abstraction would use the attraction somehow, and just make the explanation 
circular. 
Explaining it independent of attraction would not be parrallel to the other explanation. It would explain it on a more fundamental level.
Also, the cases are not as symmetric as they may seem: Objects with opposite charges are distinct in a well defined way, while the example objects for the repelling case would be not different from one object as soon as they touch. They experience nothing different from inside one of the objects, except that they can move appart.
The third case, regarding electrically neutral bodies is quite interesting. Generally speaking, the forces that are relevant in are called cohesion if it's about the same substance on both parts, or adhesion if it's about different substances. Both refer to multiple independant mechanisms causing attraction between touching surfaces - and some of these are based on attracting electric charges again; But not the whole object is charged - the charge is local to the molecules on the surface. 
A: I'm going to try to answer my own question, simply from thinking the matter through:
If the two objects have like and equal charges, then whatever happens to the electrons and nuclei, in terms of shifting around, in the one will happen in the other, and obviously, the result will be that in both substances, the same charges, positive or negative, will be near the surface, and the two objects will therefore repel each other. Maybe I'm missing something, but I believe it may be as simple as that.
And if two neutral objects are brought near each other, then obviously nothing at all will take place: since both objects are neutral, bringing them near each other introduces nothing new to the situation: we are simply bringing neutral atoms near some other neutral atoms!
A: 
I have read in a number of places how substances with opposite charges attract each other:
The excess electrons in the one substance repels the electrons in the other substance so that they move away from the surface, leaving the protons closer to the surface which are then attracted to the excess electrons in the one surface.

Your prescription is not clear. Let us take a clear example , two balls, hanging by  a string close to each other.
One is charged positively, the other is charged negatively  ( i.e. opposite charges). The negatively charged one is so because somehow ( another story) we gave it extra electrons which are sitting on the surface and creating the negative charge destroying neutrality. The other is positive because we have taken electrons and destroyed the neutrality ( equal nucleon charges to electron charges around the atoms of the material), and the positive predominates. The balls are attracted because opposite charges attract.
If we make the second ball negative too, then both balls will have excess electrons and the same charges will repell. If both balls are made positive again, same charges repel. This is an observational fact that led us to the discovery of charge and finally electrodynamics.
Neutral objects , i.e. the uncharged two balls will stay put, though many substances, not in the geometry of two balls given above, when brought close together will show adhesive or even repulsive behavior ( water repellants for example) , due to spill over forces as the shapes of atoms and molecules of matter allow this. That is why we have matter in bulk, from cohesive spill over electric and magnetic forces in the neutral bulk.
