On smaller rivers in whitewater kayaks, we really wouldn't use this procedure.  It is usually best to get back on shore if possible or get assistance from someone else.  Sea/touring kayakers often get more spread out and need a way to re-enter their boats on their own.  A key piece of equipment is the paddle float.  You can attach this to one end of the paddle, inflate, and secure or hold on the uprighted kayak.  The paddle float acts as a vert stable outrigger.  Once in place, you can use the paddle to climb back in the cockpit facing towards the rear kissing the back deck.  Once on top, spin the body to face upwards and secure yourself in the kayak.  Hopefully you have a pump handy to empty as much water as is feasible.  Here is a good demo with explanation on this procedure: Deep water re-entry.