Le Chatelier's Principle applies to steady state systems; to use it, you must first understand the 2 main types of equilibrium. Look at any object on your desk. Gravity is pulling down on it while the normal force from your desk is pushing up on it. A system that appears to be doing nothing is in equilibrium, meaning there are opposing forces--equal but opposite--that are balancing each other out. In the case of an object at rest on a desk, the equilibrium is said to be static.
Consider a bottle of soda. The carbonation in soda is caused by carbon dioxide dissolved in the soda's water. In a closed bottle of soda, carbon dioxide molecules are continually being gassed off by the liquid. At the same time, and at an equal rate, different carbon dioxide molecules are being dissolved back into the soda water. This is dynamic equilibrium, when 2 processes (1 being the reverse of the other) occur in a way that they balance each other out. Le Chatelier's Principle applies to systems in dynamic equilibrium.
Think about the formal definition of Le Chatelier's Principle: "If a system is at [dynamic] equilibrium and a change is made in the conditions, the equilibrium adjusts so as to oppose the change." This says that if we act on a system in dynamic equilibrium, the system will respond in a way to try to correct what we did to it; it will try to get back to where it was.
Apply Le Chatelier's Principle to everyday things. For example, ice water at 32 degrees F. Ice water is an example of a dynamic equilibrium with water freezing and melting constantly. It is known that ice absorbs heat when it melts and releases heat when it freezes. If we take heat away from a glass of ice water by putting it in the freezer, the system will try to replace the heat by freezing more water.
Consider again the bottle of soda. At a given temperature, there is a balance of carbon dioxide in the soda water and the pressure of the gas above it. If we relieve the pressure above the soda by opening the container, Le Chatelier says the soda will try to replace that pressure any way it can; in this case, by gassing off more carbon dioxide. This is why soda fizzes when you open it. After a few moments of being opened, the soda is in a new equilibrium with the non-pressurized air above it.
Imagine a chemical reaction that produces a gas, like vinegar and baking soda. When you mix the 2 together, they react trying to achieve equilibrium. You can manipulate the way they react by controlling the reaction surroundings. For example, what if you mixed baking soda and vinegar under high pressure? If they react with each other, the pressure would only go higher, so they react little. If, on the other hand, they are reacted under low pressure, the reaction would proceed quickly and completely to relieve the "stress" of low pressure.