Torque Sensor
The best method by far is the torque sensor. A good torque sensor will simply amplify your own strength. Let's say you have it set to a 50% increase. This would mean if you put 100 pounds of pressure into the pedals with your legs, the motor would add another 50 for a total of 150 pounds. You feel like a super hero. This is the most natural feeling method of 'assist' available. This is the method we use on the U-district and the Rodriguez eBikes.
Cadence Sensor
Another device the other companies use is the cadence sensor. With this method, when you begin to pedal, the motor kicks in until your pedals are turning at a pre-programmed RPM (revolutions per minute). For instance, if you have it programmed for pedaling at a cadence of 90 RMP, it will run until you exceed 90 RMP. If this sounds to you like it would produce a 'jerky', unnatural pedaling feel, you would be correct. That being said, it's still more natural feeling than the 3rd method.
Simple Throttle
The most primitive method is just a simple throttle (like a motorcycle has). You just use your thumb to push a lever down and the motor takes off. This is not a natural feel if your goal is to have a bicycle with some help. It is more like a motorcycle.