Use plastic zip-close bags for anything that needs to stay dry in the rain. Put a couple of pieces of paper towel in one of the bags in case you need it. If you have a seat bag, it will get wet so don't forget to put important things in that bag in plastic.

Fenders will help a lot. I have SKS Race Blades which attach quickly and easily to a road bike. I think Planet Bikes make a similar fender.

My main problem in the rain is keeping it out of my eyes. A helmet visor or hat with brim under your helmet should help with that.