When I take my friends out to a sushi bar, many of them are really conscious about whether they are eating it "the right way" or not.

I usually say "just enjoy it, any way you like". But if you are still concerned about it, then here's a set of illustrations by a Ne York-based graphic designer Peter Arkle:

While I don't feel that one must follow everything here, but there is some logic behind some of this. In case of nigiri, for example, the point is to taste and enjoy the fish. So if you soak the rice with soy sauce too much then you're not going to enjoy the flavor of the fish. The same reason apply when you place the fish side on your tongue.

But if you are going to some cheap sushi shops - I might break some of these rules. The fish might not be super fresh, so I might dip the sushi in soy sauce full of wasabi or eat the sushi with ginger so that all the fishiness dissipate in my mouth. It all depends on the situation, I guess.