I've been playing for a year now, and I just barely figured this out (although I just recently gave myself the time to figure it out). Its not going to come over night, but if you practice enough this will all start to make sense. Much like any other shooting/passing suggestions, little will make sense until YOU can figure it out physically.
Anyway, I figured it out in my backyard. I took a plastic workstation computer chair mat and used it as my surface (if you want to simulate ice a bit better, you can use any form of water-based lubrication (slightly muddy water works well, but its messy). So just like these guys all said, you really need to get your body low and your weight on your right leg (I'm a lefty shooter too). Angle your stick about 45 degrees to the ground, and the idea of getting under the puck is to get it to roll on the blade. Since you can't use your core muscles for the backhand nearly as much as you can with your forehand shots, your best bet for power and accuracy is using the blade as leverage. You'll get a good spin on it too.
Oh, and the mention to get your palms up - You know when your just coasting along the ice with both hands on the stick, with your blade pointing up? Now just rotate your wrists until the blade is pointing backwards, thats the idea behind the palms up on the follow through - just keep in mind the directing of your toe blade is where the puck is going.
Once you figure out how to get some power, you'll figure out how to get it higher and higher, with the same power. By the end of my messing around in the yard I was putting holes in the wood paneling I was using as my target.
ONE MORE THING TO KEEP IN MIND! practicing off ice can be deceiving - always keep in mind there is much less friction on the ice so you'll have to make some adjustments once your on it. Don't get disgruntled, you've already figured out the muscle movement portion, you'll just have to make subtle adjustments.
Hope all this helps!