How should I prepare a steel door for painting?
You might need to use more than soap and water - but that would be a first step. However, you don't want anything too harsh. Just makes sure that the surface is completely dry before painting.

An additional coat of primer might be worth it - but only if there are any places where the original primer has rubbed off or you have knocked the door. Places where the metal has been exposed should be sanded to remove any rust.

If the primer is sound then you should only need to undercoat before applying the gloss to give the finish some "body". I normally end up with 2 coats of top coat to give an even finish.