Sail Trim
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Trimming a sailboat is the delicate art of balacing many physical forces to acheive optimal sailing performance.
Basic Sailing Physics
Before we look at trimming, it's helpful to understand the basic physics of sailing. Imagine first that you decided to build a simple sailboat. You might take a little rowboat-shapred hull and stick a pole in the center and attach a piece of cloth to it. You even attach a rudder to the back so you can steer. You'd discover that the cloth was just flapping in the wind. So, you would need a way to angle the cloth so it was facing in to the wind and to stretch it out. So, you'd attach a second pole, called a "boom". Now the wind can exert force on your boat. We can integrate over the force being applied to the sail and treat it as having a point called the "center of effort". For now, we'll keep the sail completely facing the wind.
So, you take your sailboat, throw it in the water, and jump in. Unfortunately, no matter what you do, you just end up going whichever way the wind is blowing. You can go straight downwind but to get home you want to go upwind. If you turn the boat sideways to the wind, it still slips backwards.
To fix this, the boat has a keel which, to simplyify, is a large flat area under the boat. The water resists this movement. We treat the keel as the "center of lateral resistance".
We now keep only the forward component of the boat's movement. So, you can now go anywhere, right? No. So far you can only go in directions that are vaguely downwind (up to 90 degrees to the wind). But that's all physics says you can do, right? Actually, while you can't sail directly in to the wind, you can sail at a pretty close angle to the wind, generally up to 45 degrees.
A sail is designed that when it is filled, it forms the shape of an airfoil, like an aircraft wing. It is the effect of the wind across this shape that provides the primary driving force for the vessle, in some cases allowing it to travel faster than the wind. If the sail is pulled in too tightly, the airfoil will stall and be much less effective. Running (sailing with the wind directly behind) is the only point of sail where this is not true, with the sail acting to catch the wind like a bag. This is far less efficient and provides less driving force than sailing off the wind, so most boats set additional sails when heading downwind.
Basic Sail Trim
While sailboats have dozens of controls that affect all sorts of things about the position and shape of sails, the basic idea of trimming a boat is that for whatever angle you're at to the wind, you need to figure out how far to let out the sails.
First, the sail needs to be on the opposite side of the boat that the wind is blowing over. Then, the sail needs to be at the corrent angle. If the wind is directly behind you, the sail will be all the way out. When you're headed as close to the wind as the boat can get, you pull the sail in quite tight (that's why it's called "close hauled"). At other points, it will be somewhere in between. While it takes a little experience to findthe optimal trim, a good rule of thumb is to let the sail out until it just starts flapping (called luffing) and then pull it in till just past where is stops luffing. If you turn the boat or the wind shifts, you have to re-set the sails.
In practice most boats have little streamers on the sails called "telltales" which help sailors visualize the airflow over the sail.
There are several more detailed guides to sail trim on the net and there's a nice simulator so you can try it from your computer!