1. Sailing. If you have a decent tail wind, hold your umbrella out in front of you and steer with your rudder or by putting your kayak on its edge.
If you're crafty, you can rig your umbrella up so you can sail and paddle at the same time.
2. Shade. You can rig up your umbrella behind your back for some shade while you paddle. I stuck mine down the back of my PFD.
I store my umbrella on the deck of my kayak under the rigging for quick deployment.
If you decide to take an umbrella next time you go, make sure you get a nice golf style umbrella. If you don't get a sturdy one, and you try to sail with it, the wind will just flip it out and break it. A big nice golf umbrella works brilliantly as a sail. I also suggest buying a clear one so you can see where you're going. We had a few near collisions with duck blinds due to umbrella blockage.
More sea kayaking tips from Ali:
Clothes for warm weather sea kayaking