How to use drop handlebars properly?
There are 3 basic hand positions that most people use on a drop bar:

On the Hoods - This position allows you to reach the brakes and shifters without moving your hands and allows a fairly upright, and comfortable body position. Most riders spend 75-90% of their miles in this position.

On the Drops - This position is ideal for more aerodynamic body positions, or more athletic efforts. When you want to go hard, go here. You can reach brakes and shifters, but may have to move your hands, depending on your setup. This is generally used for descending long hills, or an aggressive position. It is less stable, and it is used for maybe 10% or less of most riders' mileage.

On the Tops - This position allows a comfortable alternative position for more relaxed riding. It is generally used when going at an easy pace, and in situations where you are certain of the road conditions, traffic and other hazards. You definitely can not reach the brakes or shifters from this position without moving your hands. It is less stable due to narrower hand position, though it may not feel like it. Most riders use it as a cool down position for 10% or so of their mileage.