Pedal extensions for one-legged bikers
There are many ways to approach this problem.  The WORST thing you can do is not involve the rider in the decision making process.

If the rider is comfortable riding, perhaps all you need is a regular bike with a toe clip (as pictured) or a clipless MTB shoe with a cleat underneat, and a matching pedal.   SPD would be the most commonly known style.

There's no need to remove the other-side crank although that is a good theft deterrent.  In fact it may help to add a little weight to the empty pedal.

A little wheel on the off side is likely to hook on things or cause more problems than it solves.

More spendy options exist too - 

Tricycle  Solving the balance problem by adding a big third wheel instead of little kids one.



Handcycle  These are powered totally by the rider's arms, not by the feet (foot)  This one is probably a tricycle, but the theory works the same for a 2 wheeled bike.



Here's a handcycle built onto a wheelchair - its possible to remove the front part and return it to normal wheelchair mode.



Prosthetic Depending on how much of the leg is missing, its possible to have a strapon leg that rides like normal.  Above-knee amputee's comments or this guy who rode the Haute Route with one leg and one arm