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Step 1
First know what you are dropping off. If you are dropping onto flat then it is different to dropping onto an incline. If you are dropping onto an incline then check if there is something you need to clear or not? Each of these three types of drops requires some basic techniques in common but differ slightly in their approach in terms of take off and landing. In all keep your saddle as low as it will go and wear as much amour as you can. We will deal with each one in turn.

Step 2 (all approaches)
First approach the drop with some decent speed and crouched but off the saddle moving your body with the momentum of the bike. High speed is not necessary but you want some speed to ensure the bike clears the drop. Around a normal running speed is fine. Pedal near to the last few feet of the drop. Like with many biking techniques it is good to stop pedaling the last few feet in order to ensure your bike is steady and you are focused on your bike for the maneuver just to come. Have your feet parallel on your pedals.

Step 3 (Dropping to a Flat surface)
Just as you approach the lip of the drop get your body central to the bike. As you approach the lip you are going to create a spring effect. The next bit is done quickly in succession in a spring like flowing movement. Your body slings forward and you then you sling yourself to the back of the bike. You lift your front handlebars as you do this and dig your feet into the pedals. Your front wheel will lift and your back wheel will carry you over the drop landing back wheel first on the flat surface.

Step 3 (Dropping to an incline)
This again can be down a mountain or off a ladder drop in a bike park. The best way down and to maintain the most speed is to let your bike get down the fastest and most natural way possible. The larger the drop the faster you want to be going to ensure your whole bike flies off and covers the distance to clear the launch platform.

As you approach the lip, get your body weight to the back of the bike crouching behind it. Past the saddle is fine. As you start to go over the lip push your handlebars out (i.e. arms pretty near outstretched). This will get your front wheel over and onto the ground as soon as you can (the objective). As you land your legs should be slightly outstretched to give you some cushion for the impact. Your bike needs to land in the same incline as the incline of the hill. Hence this is front wheel or both wheels first (not back wheel first like a flat landing). Your bike will flow with the transition down the hill.

(image courtesy of phatboyian)

Step 3 (Dropping to an incline with objects to clear)
This is exactly the same as the previous example with one main difference. Although you may lose a bit of speed you create a slight hop just before leaving the lip. This will give you the extra height and distance to clear the object. The larger the distance you need to clear the slightly higher the hop.

Amazing as it seems all these simple techniques are the same regardless of the height of the drop. So work your way up to bigger and bigger drops and bigger and bigger grins.