Hang a towel from the inside of your umbrella to use for your hands. It works great!!!
I bring an umbrella, baggies for everything including a baggie of extra towels, baggie for your scorecard, baggie for your wallet and anything else you don't want wet. Also I wear BDU's that you can buy at the Army surplus store. They are relatively waterproof and dry out fast. Waterproof work boots(if you can stand wearing boots, takes some getting used to). Screw anything long sleeve as long as it is warm enough(wet sleeves just get in the way).
Also my Gateway Bag is waterproof, and I bought a large sheet of thin hard plastic that I cut to fit the bottom of the bag. It adds even more protection from seaping water. I carry a tripod stool to sit on, while I am waiting, that way everything stays under the umbrella.
At the recent Lexington Open I was the only one on my card with dry discs. It poured from the time we started until we were done. The last 5 of 6 holes I was walking in water half way up my boots yet I remained fairly dry. Can't say I was totally dry but dry enough to remain focused. None of my discs were wet though!
i throw more forehand in the wet conditions. slippery tee boxes and slippery lies effect me much less with a one step or no step sidearm. i also tend to slow down some and stay away from my really overstable drivers