First of all, there isn't any one true way to eat sushi, you can eat it however you want. The point is to have fun and enjoy your food and company, but as far as I can tell, this is the proper etiquette to follow.
If you are at a good sushi bar, when you sit down you will find a pair of chopsticks, connected to each other at one end. They should be detached from each other before you use them. On the right of your setting should be a ceramic saucer for soy sauce. The soy sauce itself will be in a lidded jug. There will also be a little ceramic block for you to place the rounded end of your chopsticks on when you are not using them. The chopsticks should be placed parallel to the front of the bar.
When you first snap apart your chopsticks, you may be tempted to rub them together to remove splinters like Deckard did in Blade Runner. This is poor form since a good restaurant should give you sticks made of wood that won't splinter.
When your sushi is served, it will come with some green wasabi (very spicy stuff, be careful!) and slices of ginger. You can mix a little of the wasabi in your soy sauce to bring out the flavor of the fish if you want. The ginger is intended to be eaten between pieces to clear the palate, and provide something to nibble on. I've seen many people put pieces of ginger on the sushi itself as they eat it, or spread wasabi on individual pieces. This is wrong.
Sushi is supposed to be eaten with the fingers, but you can use your chopsticks instead, just be careful to not drop the sushi. You are supposed to flip the sushi over and dip it in the soy sauce fish side down, and then place it in your mouth fish side down. Many people tend to dip the rice side into their soy sauce, which can lead to the rice falling apart. Try not to place a partially eaten piece of sushi back on your plate, you are expected to eat the whole thing once you pick it up.
Never pass food to someone else using chopsticks, instead you should pass them the whole plate and let them pick from it. When taking food from a shared plate, you should use the reverse ends of your chopsticks.
Don't smoke at the sushi bar, it will ruin the subtle flavors of the fish for yourself and others. There may be an ashtray present at the bar, but to use it is dismissive of the efforts of the chef.
Try to eat all of your sushi, it is considered poor form to leave uneaten food. When you are done eating, place your chopsticks on your soy saucer parallel to the front of the bar, this is a signal to the waiter that you are done.
The waiter will take care of your check and your money, the chef is not expected to handle money. When you tip, take the effort of the chef into consideration, since he will be sharing in the tip.