Overspin down hills.
One pedalling drill you can do on any Ride with downhills is spinning the pedals as quickly as possible as you accelerate down slopes. To do this correctly, leave the bike in a gear that's too easy, one that forces you to spin the pedals to keep up with the speed of the bike. Your goal is to rev your legs as quickly as you can while remaining seated. At first, you'll probably bounce a lot on the seat. But, with practice, you should be able to stay in the seat and maintain a calm upper body even though your legs are spinning at supersonic speed. If you do this drill a lot, your pedalling speed and efficiency will quickly improve. You can also do this drill with a tail wind.

Rollers are great!
A great way to smooth your spin is to train on indoor rollers. Rollers are seen a lot at track events and are used for warming up on. You sometimes see them at road events as well. Rollers consist of a frame with three spinning drums (one for the front wheel, two for the rear), with a rubber belt connecting the front drum to one of the rear drums. You put your bike on the rollers and start to pedal and you can balance and ride just like you do spinning down the road outside. Most rollers have optional equipment that allows increasing resistance because there isn't much drag from just the roller unit itself. This resistance unit is not required to develop your pedalling efficiency though as you only need light resistance.

Rollers require above-average balance and exaggerate any pedalling flaws. With enough practice, you naturally eliminate pedalling problems because they're so noticeable. And then, you ride faster with the same effort because your pedalling becomes more efficient and more of your energy goes into driving the bike.

Ride Fixed Gear
A few decades ago fixed gear bikes were commonly used as an important training tool to build base pre season. They are becoming more popular these days. Especially in places where there aren't many hills. Fixed gear is great because it trains you to over rev when going down hills just like what I mentioned above. On a fixed gear bike you can't coast so constant pedalling is required everywhere you ride. You must accelerate pedal speed on downhills because you can't shift gears.

These factors combine to smooth your pedal stroke and force you to spin complete circles. Pick ride routes that avoid steep climbs and descents. You don't need to buy a new bike to pull this one off, either. A threaded-hub wheel, a track cog, a BMX chain and a few axle spacing tricks can Turn your regular bike into a fixed-gear special. Fixed gear bikes can be picked up for less than $1000. The ideal gear for them is somewhere between a 66" and 72".

Try The Track
If you're one of the privileged few who can ride a track bike at a velodrome (a circular, banked track for cycling), you'll reap the same benefits as training on a fixed-gear bike. Never ride a track bike on the road without breaks though.