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.