This is the best way. I am a mountain and ice climber (though not so active at it anymore). A "mountaineers' coil" as sketched above is an excellent way to coil a cord (or rope) without kinking. It is very easy to do and fast once you get the pattern down.
But cgrutt left off a very important "step 0" before making the coil. You must first "stack" the cord and start from the midpoint. You do this as follows. You first grab one end of the cord. Work out all kinks. Then starting from one end with the end outside (or in your hand) *stack* the unkinked cord till you reach the other end. Then with both ends in your hand (cord doubled up) stack again till you reach the midpoint of the coil. Then make the Mountaineer's coil making loops back and forth with your hand from the midpoint . You can find rock climbing tutorial videos of this online or look at books on mountaineering and rock climbing (Freedom of the Hills is excellent). It is exactly the same procedure for electrical cords as with ropes. But it is critically important to start out with an unkinked cord and cords kink easier than rope. If you do and keep doing this every time, the cord will remain kink free. Also, if correctly worked and stacked, you will find with each successive coiling that it gets less kinked with each successive use as you get it properly worked.
NEVER EVER NEVER roll a cord winding loops from elbow to hand. When you do this, it puts an overall rotation each turn and generates kinks that have to be worked out.
Rock climbers and mountaineers are often super good and fast at this procedure since it can be life and death on a multi-pitch route to avoid rope snarls. Kinks can also catch on features generating all sorts of problems. Climbing partners will also murder anyone who *$%# -up the rope -- so it gets very ingrained.
Also, I strongly recommend avoiding plastic sheath cords. Those kink too easily. Rubber sheaths are much better. Also, working in low temps can exacerbate kink problems (especially with plastic sheath cords). Below freezing can be nightmarish and it can be better to take the cord inside and let it warm up first before coiling.
Be kind to your cords and your cords will be kind to you

Maybe your life does not depend on it in DIY and even job site applications for cords as it does for mountain climbers. But the methods mountaineers use really help. I gather some contractors are very phobic about cord handling also since poor techniques can create problems and inefficiencies on jobs.