This article refers to the machines for washing dishes. For the people that wash dishes, see here.
Modern mechanical dishwashers can be a great time-saver in the kitchen. Improper use however, can lead to much time wasted on dishes not washed properly, or worse, irreparably damaged dishes. The three key points to loading a dishwasher are placement, material, and detergent.
Dishes do not have to be arduously rinsed before placing them in the machine, for this would defeat the point of having a machine. They do however need to have any large chunks of food scraped off them. Obviously start from the back, and work your way forwards when loading the dishes, but this is mostly for ergonomic reasons. Dishwashers have racks for a reason, use them. Plates, bowls, etc are meant to go vertically so that water runs off them rather than pooling, Most washers employ a technique that involves a rotating arm on which are mounted jets of hot water. Enough gap must be left between dishes to allow these jets of water to do their job. Don't stack them too far apart though, otherwise you will waste space in the load. Dishes should generally face inwards. Be sure that nothing sticks out and gets caught on the sides of the machine, as this may damage both your dishes and the machine. You probably have a special container for cutlery. As with everything else, your cutlery should be placed to maximise its exposure to the washing spray. A tip from NanceMuse: alternate the orientation of the pieces so that the heads don't get caught or stuck in each other. The top rack is usually shallower, and is designed for mugs, glasses, etc. The washing action here is gentler. If you have plastic items, they go here. Put them in the bottom rack, and they can warp.
Unlike a microwave oven, metal is fine in a dishwasher. Certain types of plastic however can melt or at least deform in a washer. Check for a "Dishwasher Safe" stamp on the item before putting it in.
There are a number of different types of detergent for use in dishwashers. This should say enough on the subject. The detergent goes in a dispenser on the back of the front door/panel (excepting some top-loading washers). Ensure the cover flap on the dispenser is closed before starting the machine, and make sure you don't put the detergent in the one meant for rinse-aid.
I hope this helps some first-time users. I've only recently used a washer for the first time in my life.
This node is dedicated to OldMiner, who wonders why I haven't noded in a while.