I began using this rig in 2001 and have had a lot of success with it. The rig is highly effective, because it allows you to get a bait suspended off the bottom at a depth where fish are feeding, where baitfish are suspended, or just above vegetation.
Here are some specifics on how I rig for dropshotting:
I prefer fluorocarbon line in six to ten pound test. This is low-stretch, highly sensitive line that allows me to feel the bait as I shake it, and detect bites.
I like the Gamakatsu #1 or #2 drop shot hooks. I'm hooking 99 percent of the fish that bite, including wipers on live bait.
A number of 3" to 4" soft plastic finesse baits will work. I'm using the Berkley Drop Shot Bass Minnow and Drop Shot Worm, and the Bass Assassin Baby Assassin. This rig is great with live bait too.
Splitshot or dropshot weights from 1/16 oz. to 1/2 oz. will allow you to get the bait down.
Tie your hook using a Palomar knot and leave a tag of at least 24 inches. Pinch on your lead shot and tie an over hand know beneath it to hold it at the proper depth or use a dropshot weight on the tag end of the line. Use the least amount of weight you can get away with based on wind conditions. (See diagram below)
Hook plastic baits through the nose or head, so they'll suspend horizontally. Fish the bait vertically beneath the boat, allowing the shot to fall to the desired depth. Make the bait jiggle in place by shaking your rod tip. If you get hung up, a slight tug on the line should pull the weight free or strip it from the line. Just add another piece of lead and quickly get back to fishing.
This technique works best in clear water situations, but I've done well in stained water too. Don't limit yourself to strictly vertical fishing though. You can also cast this rig to shallow water and work it slowly back to the boat with good results.
See below for an illustration of a dropshot rig setup.