Finding yourself upside down in a kayak can be a disconcerting experience. Getting yourself back upright is literally a snap (hip-snap that is). There is so much to fuddle your brain when you flip your yak. First you're upside down. Then, the double bladed paddle adds to your confusion. Finally, the paddle stroke you need to do is upside down from the way you normally paddle. Now, this guy below shows how it's done. He's in a pool of known depth, so he's not wearing a helmet. It's better to practice with the helmet to get used to the extra drag.
Once you are upside you’ll experience confusion since the world has gone upside down. Take a second to get your bearings. To flip back up, you’ll have to push down on the water – what to you, being upside down, will feel all wrong. You’ll probably need to pause to reorient yourself until the skill becomes second nature to you. Katrina here is practicing in a pool for photographic purposes, and doesn't have a helmet. She is shown below practicing in more realistic conditions. Note the helmet.
Bring your head up near the water surface on the side you’ll be rolling up on. Get your head above the forward blade, so that it feels like you are pressing down again when you sweep the forward blade wide and backward. Bring your trailing elbow in close to your body so the trailing blade tips up out of the water and doesn’t drag.
The Sweep and Snap
Begin to sweep the blade wide and toward the stern of the boat. As you sweep, pressing downward and backward, snap your hips so your body tilts to the opposite side. This rotates the hull of the boat upward and starts it rolling the right direction Resist the urge to bring up your head till you complete the hip snap. Keep pulling the sweep as you snap your hips.
As the hull rolls up, press hard on the end of the sweep stroke and let your body be pushed out of the water and back to the vertical position. The boat will jump forward. Immediately bring the opposite blade down and take a strong stroke to get the boat moving and stabilized.
Practice this a lot. It should become second nature so that you pop back up almost without thinking about it. There are three other standard ways to do this or you can make up your own way, but this method is the easiest, requires less finesse, balance and physical strength to perform (a natural choice for big awkward klutzes like me then).
Always wear a helmet when kayaking and especially when practicing this skill. In the river, it’s even more important because the bottom can be rocky and quite close to your face. Also, helmets don’t bleed and attract piranha, gators or those big mosquitoes they grow here in East Texas.
These links show how to perform the standard roll.
Gorp: Four Elements of The Kayak Roll
Aquabatics Kayak School: Sweep Roll Tutorial
Patagonia Kayak School: Kayak Roll Identifier and Troubleshooter