In the rain I like to reduce air pressure in the tires a bit (5-10 psi) to give a bit more traction, avoid making turning/breaking maneuvers on road paint, wear a cycling cap under bike helmet to keep water from glassess/eyes, assess braking conditions early in the ride as it will take longer to stop with wet brakes, do not follow too closely to people in front as tire spray is annoying, anticipate when you need to brake and lightly apply pressure to brake levers to squeegee brake tracks.
I like to think of winter driving when riding in the rain.
Forget staying completely dry as if you get so waterproofed when you start exerting yourself you will get wet with sweat anyway. But as Kerry stated, depending on the temperature staying warm can be critical. I would also suggest keeping a towel or two and dry clothes in the car to change into after the ride as driving home in wet/muddy clothes is not pleasant.