Caution: This is a movement that requires a great deal of balance so if you suffer from balance problems you may wish to either avoid it or just use your own bodyweight while holding on to a fixed object. Definitely never perform with a barbell on your back if you suffer from balance issues.
Variations: There are several ways to perform the exercise.
One way is to alternate each leg. For instance do one repetition with the right, then the left, then the right and so on.
The other way is to do what I call a static lunge where your starting position is with one of your feet already forward. In this case, you just go up and down from that starting position until you are done with the recommended amount of repetitions. Then you switch legs and do the same.
A more challenging version is the walking lunges where you walk across the room but in a lunging fashion. For walking lunges the leg being left back has to be brought forward after the lunging action has happened in order to continue moving ahead. This version is reserved for the most advanced athletes.
Lunges can be performed with dumbbells as described above or with a barbell on the back, though the barbell variety is better suited for the advanced athletes who have mastered the exercise and no longer have balance issues.