Manipulating Equilibrium

Because equilibrium is a dynamic, thermodynamic process, there are a number of things we can do to "fiddle with" equilibrium systems.  Perhaps the most significant conceptual tool we have at our disposal is LeChatelier's Principle.  {Side note: To the francophones in the audience, I believe the "a" in "LeChatelier" is supposed to have a little hat on it...}
When a system at equilibrium experiences a stress, the position of that equilibrium will shift to relieve the stress (as much as is possible).
What's stress?  The most common type of stress we're likely to see in chemical reactions is adding or removing a reactant or product.  Let's think about the simple equilibrium reaction 2A↔B.  The equilibrium constant is:

If we add a little extra "A" to the reaction after equilibrium has been established (a stress), the reaction will have to shift toward the products to re-establish equilibrium.  If we look at the reaction quotient, Q, for a reaction, we can evaluate whether a system is at equilibrium, and if it is not, what direction the system has to shift to reach equilibrium.  The reaction quotient has the same mathematical form as the equilibrium constant; if Q if less than K, then there are too many reactants in the system and it must shift toward products.  If Q is greater than K, then there are too many products and the system must shift toward reactants.