Fixed gear pedaling

Question
I would like to know some tips as to pedal and ride more efficiently. I am riding a fixed gear with toe clips.

Answer
Christopher,
Excellent question!  Fixed gear riding puts a premium on smooth application of force around the entire pedal circle.  To apply smoothly, you have to be solidly strapped in to the clips and work on pushing and pulling simultaneously.  This doesn't mean just push down and pull up.  It means push down, pull across the bottom of the pedal stroke (from about 5 o'clock to  7 o'clock), pull up, push over the top (from 10 o'clock to 2 o'clock) and then push down again.  
In my opinion, the best place to really practice is in a spin class that encourages you to spin at higher rpms (90 rpms or more).  In spin class you can really concentrate on your mechanics (sequencing your muscle movements) and work on making smooth pedal circles.

I hope this helps
The most helpful visualization to make pedaling more efficient is to imagine that as your cadence increases, you are trying to press the crankarm inwards towards the bottom bracket(seemingly shortening it) as you pedal, thereby turning the pedals in smaller and smaller circles.  Of course, you won't be able to actually crush the crankarm, but imagining doing it will trigger your muscles just a little bit sooner than mentally trying to coordinate the movements.