A technique which may help you get a more efficient pedaling stroke is an exercise called isolated leg .
With your bicycle on a trainer or on a slight uphill, unclip your left leg and pedal using only your right leg for 30-60 strokes.
Then switch and do the same for your other leg.
This exercise will give a very natural feel to how your legs should be rotating to achieve an efficient pedaling stroke.
bicycles.stackexchange.com/users/120/peppajiggapuff
I was told to imagine that you are trying to scrape some mud off your foot.
As you pull down from about 1 O'Clock, just as you reach about 5 O'Clock, start to pull your foot back, pointing your toes towards the ground, like trying to scrape some mud off the front of your shoe.
I am not too sure where you should stop this pulling, but I would say it is about 8 O'Clock, since by that stage your other foot should be starting to put some pressure on the other crank.
bicycles.stackexchange.com/users/106/Anthony K
Mountain Biking is the best thing.
Was just reading a training article by Chris Carmicheal (trained Lance Armstrong) and in studies he did mountain bikers had the best natural spin.
They figure it came from climbing on loose dirt while seated to make sure you had good traction.
Another good exercise is to pedal with one foot.
I do this once a week at the end of a ride.
Only for a block or two
but it really emphasizes the lack of pedaling in a circle.
bicycles.stackexchange.com/users/30/curtismchale
I find that the best time to practice making good circular rotations is when I am completely out of gear (doing 20mph in the granny gear, for example).
I ride a single speed, so this is pretty easy for me.
Being out of gear allows me to feel how circular my movements really are.
If I'm not pulling back at the bottom of my stroke and then up the back side, I feel the bike lurching around under me.
This helped me, maybe it can help you as well.
bicycles.stackexchange.com/users/50/Jack M.
I certainly am no expert but some things that helped me a set of rollers (not a stand/trainer) but rollers can help smooth your motion "thinking in circles" helps as well.
Visualize the foot/pedal motion
bicycles.stackexchange.com/users/37/Tim
There are a couple tools (both quite expensive though) that can help.
It all comes down to muscle memory though, the more you spin the better you get at it.
Computrainer has a spin scan to help identify flat or dead spots in your cadence.
Powercranks force you into leg isolation by disconnecting the cranks from each other.
bicycles.stackexchange.com/users/2953/Glenn Gervais
If you are after smoothness, then pulling up may improve your game.
The concept that you need to pull with the upward-bound leg/pedal is a myth that has been perpetrated because it feels good!
It may be worth doing, for that reason, alone. ;]
But experts have found that max power is generated when concentrating on the downward leg while completely unweighting the other until it returns to the top of the stroke.
In order to smooth out your stroke, and locate the issues you are dealing with, doing hill repeats alternating one leg or the other will def help you find the weak spots in each leg's pedal stroke.
bicycles.stackexchange.com/users/2974/andy
I got this trick off the Internet about ten years ago.
Can't remember where, I'm afraid, or I'd credit the source.
Imagine that your feet are really hands , and that you're not pedalling, but winding yourself along some kind of rack-and-pinion track.
Picture it, feel it, and keep that motion in mind as you pedal.
Our hands are much better equipped for the right kind of push-pull motion than our feet, so thinking of winding with your hands primes your motor cortex to keep a consistent amount of force round the whole revolution.
Stay vigilant: if you notice yourself going back to piston-pedalling, just think of hands again, and you'll soon make it a habit.
bicycles.stackexchange.com/users/3512/Dan Hulme
I couple of years ago I switched from using a normal pedal to using a clipless pedal. It takes a little while to get used to. Now, to be able to use it optimally I need to learn how to pedal in circles instead of in squares, eg applying the same force during the whole rotation "orbit". What do I need to think of to be able to pedal properly?
How can I pedal in circles?
bicycles.stackexchange.com
<pedals><training><clipless>
bicycles.stackexchange.com/questions/190
bicycles.stackexchange.com/users/29/Johan Dahlin
A number of exercises are recommended for improving pedal stroke. One technique which may help in getting a more efficient pedaling stroke is an exercise called isolated leg . With the bicycle on a trainer or on a slight uphill, unclip your left leg and pedal using only your right leg for 30-60 strokes. Then switch and do the same for your other leg. Another good exercise is to pedal with one foot. In order to smooth out your stroke, and locate the issues, doing hill repeats alternating one leg or the other will definitely help find the weak spots in each leg's pedal stroke.  A varied set of techniques might help you pedal in circles. These include exercises to isolate your legs, structured foot movements, hill repeats while using each foot in turn, and pulling up. It is also a good idea to practice with mountain biking or rollers to improve your motion. Moreover, there are some specialized tools available, like Computrainer and Powercranks. Finally, visualizing your feet as hands and moving them accordingly might help you approximate an even distribution of force round a circle.
A varied set of techniques might help you pedal in circles. These include exercises to isolate your legs, structured foot movements, hill repeats while using each foot in turn, and pulling up. It is a good idea to practice with mountain biking or rollers to improve your motion. There are some specialized tools available, like Computrainer and Powercranks. Visualizing your feet as hands and moving them accordingly might help you approximate an even distribution of force round a circle.