I have a trick answer to my seemingly simple question: For the Lakers to expand Dwight's game, they should keep it simple. This means fewer feeds into the post, though many Laker fans lament the lack of Dwight Howard touches.
While I believe Howard to be a good offensive player, it's often foolish to start a possession with a pass down low. Hit Dwight on the block if he's got the seal of if he's open; if you plan on "X" amount of touches, such planning is probably flawed and bound to gum up your offense. Feeding the post should be like running the QB/RB "read option" in football: react to the situation, don't cram your preconceived plan into the situation.
For Howard to be highly successful with the Lakers, he must be an amalgam of Tyson Chandler and young Amar'e Stoudemire. In short, he must be the old version of Dwight Howard. That guy feasted on spread pick-and-roll runs to the rim and one-on-one catches with deep positioning.
Per the latter, Stan Van Gundy devised a smart way to get Dwight touches. Howard is not an incredibly tall center, but he is fast and he is strong. So SVG often had Dwight run all the way to the three-point arc to set a screen, sometimes even off the ball. If Howard isn't open on his roll to the rim, he stays with the play and often drags his defender closer to the hoop than said defender would prefer. Then, the entry pass comes.
Dwight's on-the-ball screens more often result in immediate buckets because the ball-handler is keyed on feeding Howard. When Dwight sets the screen for a ball-handler and races past, say, Al Jefferson, he's frequently in the clear for an alley-oop. Howard can easily burn coverages on high screens, and when extra attention is devoted to stopping him, it can make somebody like Jameer Nelson look like a superstar.
Dwight is best helped by a spread pick-and-roll attack, much like what New York is using right now. Of course, that puts Pau Gasol in an awkward position, but in order to get the most out of Howard, floor spacing is a must. When Dwight goes one-on-one in a crowded paint, he's not nearly as effective as when he can exploit single coverage in a spread-out defense.
Also, if that spread-out defense throws a double at Dwight, three-point opportunities abound. The Magic used this strategy to fuel one of the league's best three-point attacks. While the Lakers don't quite have snipers like J.J. Redick and Ryan Anderson, Jodie Meeks and Kobe Bryant can certainly benefit from some open shots. The trick is finding the right mix of talent to surround Dwight—or by having Pau Gasol somehow develop a three-point shot.
The Lakers would be wise to also develop Dwight Howard's shot, insofar as they can. Blake Griffin has grown a respectable long-two jumper over the past two seasons, which may mean that there's hope for Howard. As Dwight ages, it will be important for Dwight to scare defenses beyond his pick-and-roll work.
For now, keeping Dwight to a heavy pick-and-roll diet is wise. Sometimes, less is more, and a center can be more effective setting screens and catching lobs than by camping out and attempting whatever post move he learned last week. If the Lakers want to get the most out of Howard, they should work on various screens that he can run in spread-floor situations.