There is no one right way and the circumstances may render some techniques difficult or impossible. I have taken many swims in a PFD unintentionally but the majority have occurred on fast flowing rivers of in ocean beach break. In these instances, taking a long swim with a paddle only is not all that common, and when one does swim, often the swimmer has to hold onto not only a paddle but a boat as well. In that type of situation, using the paddle to assist swimming in not possible. Also, in shallower water, effective use of the paddle to swim is often not realistic.
On a river, sometimes the paddle is best tossed onto shore or into an eddy, especially if you are in a group in which multiple rescuers are coming behind. When swimming in current with a boat and paddle, I will usually try to secure the paddle in the boat whenever possible. When not, I will try to hold the paddle, and either the grab loop or painter on the boat in one hand and use the other for side stroke type arm strokes.
If you are swimming in current or in surf in which you are in danger of being swept onto rocks, you must stay upstream or outboard of the boat. In this type of scenario, you can generally only successfully maneuver yourself and boat laterally. I attach short painters to my whitewater canoes that allow me to free up a short length so that I can still hang onto the boat, but get far enough away from it to effectively kick with my legs. In this case, I am swimming in a side stroke position using one arm and both legs to propel myself.
The floating on your back type of thing with your nose and toes up works if the current or surf is propelling you in a safe direction. If you are alone and not going anywhere, you are pretty soon going to have to try something else. Also, if current is taking you directly toward something bad, like a strainer, or you are in a long continuous rapid in which you must get into an eddy, back floating is not going to be effective.
If you are in a situation in which you must actively escape the current, you are generally best off turning onto your stomach and using a crawl-type stroke to propel yourself. One whitewater open boater, swift water rescue instructor holds the T grip of his paddle in the crook between one thumb and index finger and swims trailing the shaft and blade. Sometimes it is easier to exit the current and enter and eddy by rolling over and over to the side to make lateral progress as you approach the eddy.
Best way to learn how to swim with a PFD is probably to take a swift water rescue course.