This technique is pretty simple: you lift the weight using two limbs and you lower the weight with one limb. For the leg extension, you'll lift the weight up pretty fast with both legs, lower slowly with one, then repeat, alternating legs.
Accentuating the eccentric (negative) stress will lead to more strength gains. The reasons are related to structural as well as neural adaptations. Also, the eccentric portion of a movement is the main stimulus for muscle growth as it's the cause of most of the microtrauma. This acts as the signal to kick the muscle-building process into overdrive.
The weight during the lowering portion of the exercise is twice as high as during the lifting portion. The load to use should be light enough so that you can accelerate it during the lifting but heavy enough to make the single-limb lowering portion hard to do. A load of around 70% of your maximum two-limb result is a good place to start.
The lifting portion should be done as fast as possible while the lowering portion is to be executed in about five seconds. Sets of three to five reps per limb are performed (so six to ten total reps per set).
This technique also works great with the hamstring curl and leg press.