Upward force on a object at rest Is there an upward force on a object at rest? If yes, where does it come from?
 A: Yes, it's called the normal force.  It comes from the rigidity of the stuff separating the object from the center of gravitational attraction, i.e. the rigidity of the rocks, dirt, floor, table, etc.  If you'd like, you could think of this stuff as behaving like a spring with a huge spring constant.
Any first-year physics textbook will cover this; there's a very incomplete list of books in another question.
A: It is all electrostatics. The electrons on the outer shells of the atoms of the object don't want to be anywhere near the electrons of the atoms on the resting surface providing a repelling force which increases with proximity. When this force balances with gravity you have reached "equilibrium". In fact, everything is somewhat fluid as the atoms move and vibrate nothing is really static. But on a macroscopic scale it is unnoticeable.
A: The upward force on an object at rest is called the Normal force and is always perpendicular to the surface. If you recall from Newton's Third law, "Every action has an equal and opposite reaction." 
So an example is a block sitting on a table. The block is exerting a force DOWN on the table from the gravitational force, its weight. By Newton's Third law, there is an equal an opposite reaction due to this downward force. The block is "pushing" down on the table, so the table must also push UP on the block. This pushing from the table is the normal force. If this force were not present, the block would accelerate right through the table due to Newton's Second Law.
A: Lennard-Jones potential is a big answer to the confusion

The force is a spacial deriviative of the energy, F = dE/dr. So, positive derivative, where plot goes up you get attractive force, and where it goes down you will have repulsion. You see that there is a huge reuplsion between atoms when the distance between them, r, is very small. So, they cannot be pulled very closely. As gravity pulls book to the molecules of table, they repel very strongly. Atoms tend to stay at distance $r_m$, producing molecular structures. Please note that the repulisve force appears at distances smaller than distance between molecules. So, you do not feel it normally, when keep your book is above the table. The reaction force is zero at that distance. 
You can make it visible at visible distances, though, by chaining zillions of atoms in one chain. Then, when you compress the chain by 1 mm, the distance between atoms varies by fraction of $r_m$. You get into the parabolic potential well $r_m$. You call such setup a spring. You expand it - you see that atoms attract. You contract it -- and see that they repel.
