Here's a video featuring one of the best short game players of all time, Calvin Peete, and his tips for better short game play.
Also, pay close attention to this video by golf instructor Mario Bevilacqua, showing the different trajectory windows a player can utilize on chip and pitch shots.
Then of course, there's the video by Brian Manzella on the 'Rule of 12', which I use in almost every round.
Some have a hard time defining a 'chip' versus a 'pitch' shot. I prefer Peete's differentiation between the two with a chip shot requiring almost no wrist cocking or bending (sorta like Manzella shows in the Rule of 12 video) and the pitch shot requiring more wrist action so the golfer can get more leverage.
In general I tend to favor the Rule of 12 philosophy of trying to get the ball on the green immediately. The beauty of the Rule of 12 method is that the safe zone will be closer to the golfer and the golfer can now hit that spot more consistently. A lot of golfers will primarily chip with a SW. Hubert Green, one of the all-time great chippers, only used a SW. But, the difficulty is that if you have a 40 yard chip to the hole, you may have to your SW roughly 20 yards to a landing area. Compare that to more of the Rule of 12 method where you may be able to use a 9-iron and only have to carry the ball 5 yards to hit the 'safe area.' I think it's a lot easier to hit the spot on the green you want with a 9-iron from 5 yards away than it is with a SW from 20 yards away. Furthermore, the SW will generate more spin and often times it becomes difficult to get that correct amount of spin on the ball.
The other parts I find important are the trajectory. I think good short game play is in general about being able to understand what trajectory will work best for that shot and being anble to hit that trajectory. Again, this is where I think the Rule of 12 is useful because it can give the golfer a spot to target, now they just need to figure out what trajectory and what club to use.
Lastly, I think it's important to pay attention to and understand the terrain. Slight downhill lies can great affect your trajectory because you have such a short distance and the clubhead is traveling a higher speed, so a downhill lie usually gives golfers (myself included) trouble in recognizing the ball will fly lower that expected and that can be the difference between chipping in or leaving yourself with a 10-15 foot putt.
Recently, Rickie Fowler was in GOLF Magazine discussing some tips for hitting more greens and one of them he said was to realize that elevated greens don't spin the ball much whereas greens that are below the golfer tend to sit and spin the ball more.
I think the same concept applies with chipping and pitching. Thus, the golfer needs to factor that in when hitting a shot around the green, even when using the Rule of 12 principles.
More often than not, the green you miss will be a little elevated. That's because the elevated greens or parts of the green that are elevated are designed so that the ball will more easily roll off the green if the golfer just msises the green on the approach.
My personal rule of thumb is to start playing for more roll when the green is at my knee level or higher. Usually these shots require a SW or a LW and I wind up going to the LW more often because the ball will roll out too much with the SW. The Rule of 12 principles can still apply, but you may want to take 1-less club in this situation.