[edit] Steps

Put about 2 tablespoons of oil into a wok/frying pan. Sesame or peanut oil are preferred for their authentic Chinese flavors. Sesame oil will tend to smoke a bit more than peanut oil at high heat. If you are using frozen pot stickers, skip to number 4 and add 2 tablespoons additional water.
Heat the oil for about a minute. (You might see bubbles starting to form.)
Fry the pot stickers for about 3-5 minutes each, or until the bottoms turn brown.
Add about 1/2 cup of water and place a cover on the pan. This will allow the pot stickers to steam and cook all the way through.
Let steam until all the water is gone (you'll start to hear crackling sounds) and the pot stickers again begin to brown. If you like them well browned, gently lift and turn them with a spatula to brown the sides.
Remove from the heat and serve.

[edit] Tips

If you want, you can fry the other side.
Sauce to accompany pot stickers is a mixture of 2/3 soy sauce, 1/3 Chinese rice vinegar, fresh grated or chopped bottled/pickled ginger, and sesame oil, often with a garnish of chopped chives. If you like it spicy, add Chinese chili paste to taste. 2 other alternative dipping sauces are: 1) soy sauce, drips of sesame oil and one thin sliced garlic clove. 2) soy sauce, drips of sesame oil and rice vinegar and one diced green onion.
Serve it with soup, and you'll have a complete meal.

They're called "pot stickers" for a reason, they stick to your pots. Teflon coated frying pans or well-seasoned cast iron will minimize the difficulty in lifting and turning them.
Don't fry the pot stickers for too long or they'll turn black.
Try not to fry too many at once, or some may burn because you didn't remove them fast enough.