I'd say start with curbs--low to the ground and minimal penalty for failure.

Approach the curb in the attack position. As your front tire is nearing the edge of the curb, push the bike away from you with your hips while keeping your arms in the same position (don't jerk the front end up!). By pushing/hucking the bike away from you using your hips, the front end will naturally loft itself. This motion is very similar to initiating a wheelie. When in the drop, maintain a rearward position on the bike and drop your heels so you can absorb the impact.

Once you feel comfortable dropping a curb, you can then begin practicing on the trail--smaller roots and logs--and work your way up to the bigger stuff. The drop on Kickapoo Down needs to be taken at speed. Once you hit it right, you'll wonder why it took you so long--it's really that smooth of a transition. The "kicker" on Sugar Bottom rides more like a jump than a drop, which requires different technique. Get your drop technique down first, then you can start working on the jumping.

Practice, practice, practice.

The biggest mistake I've seen people make when learning to drop is to yank up on the front of the bike. This puts you in a horrible position for the landing and basically takes away any ability to absorb the impact and keep the rubber side down. Remember, initiate the drop using your hips and legs, not your arms and upper body. Stay light with your grip and keep your heels dropped--heavy feet, light hands. Manipulation and control of the bike all begins with the hips.

Check out Lee Likes Bikes for more info on this and other techniques - Lee Likes Bikes

*disclaimer--I give this advice because you asked for it and I know the proper technique, but that doesn't mean I have the ability to apply to the trail or equate to me being king of the trail! I make plenty of mistakes, walk an obstacle and/or crash frequently attempting, and am nowhere near being the end-all, be-all of riders in this club. Thing is, the peeps that are super gifted on the bike are just that--gifted--and they don't need to learn and practice as much as us novices do because it comes so naturally. That said, riding with peeps with mad skills goes a long way in your progression as a rider!!!