1) Riding in the hoods
This is the primary riding position for drop bars, as it allows shifting and braking. This is one of the most comfortable position to maintain over long periods of time. Not as good as the primary position for bullhorn bars, because you may tend to get numbness in the hands if you grip too tightly.
Some people like to put their index finger over the front of the shifter.
Use the 2nd and 3rd finger to push the brake lever or release lever in order to shift gears
2) In the drops
If you want to chase down a breakaway group or fight the headwind, assume this riding position. Getting into the drops of the handlebar gives you a smaller aerodynamic profile, reducing the drag acting on you. This is more obvious when you are going fast.
Braking and shifting are both possible from the drops, although shifting is a bit harder compared to from the hoods as it is difficult to exert strength in this position.
Assuming the sprinting position
Braking from the drops
3) Centre of handlebar
This gripping position is useful when climbing hills, as it gives you a bit more leverage and something to pull on when charging up the slopes. Also good as an alternative on longer rides to prevent hand numbness.
I have added cyclocross brake levers (otherwise known as interrupter levers) to allow me to brake when I am holding the centre of the handlebar. Not a necessary feature, but good to have, especially if you are used to flat handlebars. Shifting is not possible from this gripping position.
Gripping the centre of the handlebars
Braking is easy!
4) "Driving" the bicycle
An unconventional gripping position, this is. Not a primary riding position, as braking and shifting are not possible. However, it is comfortable, similar to the primary position for bullhorns. The bends help to support the palm and steering is easy, somewhat like a steering wheel in a car. Good alternative for long, uninterrupted stretches of road.
"Steering wheel" on a bicycle!
5) TT riding position
This must be one of the strangest way to "grip" a drop bar. When in this position, the hands are actually gripping thin air! However, because the side of the hands are able to push outwards against the shifters, this is actually more stable than it looks. The main advantage of this position is that it allow you to rest your elbows on the top of the handlebar, and puts you in a low aerodynamic position similar to when in the drops.
Tricky to maintain for long stretches, as it may be unstable, especially if there are crosswinds. Shifting and braking are of course not possible from this gripping position. However, this is excellent for long, unbroken stretches of nicely paved straight roads.
Push outwards with your hands to maintain good control when in this gripping position.
These are the 5 gripping positions that I use on my drop bars. When compared to bullhorns or flat handlebars, each type of handlebar has its own advantages and disadvantages.
Main Advantage of Drop Bars: Aerodynamic positions available
Main Disadvantage of Drop Bars: Less stability and control for downhills
Main Advantage of Bullhorns: Extremely comfortable
Main Disadvantage of Bullhorns: Less stability and control for downhills
Main Advantage of Flat Handlebars: Good control and stability for all terrains
Main Disadvantage of Flat Handlebars: Less comfortable for long rides, less aerodynamic
As you can see, each type of handlebar has its own merits and downsides. Depending on your riding style, you can choose the handlebar that suits you best. If you are not sure, just try another bike that has a different type of handlebar and see how it feels like!