Yakk -- you're right, the key is to learn certain "operations" -- basically the more you can memorize, the faster you get. To do it in less than 30 seconds requires memorizing about 47 different moves based on where the cube parts are
God of Thunder -- the last layer is most definitely the toughest! you gotta solve the edge pieces and then rotate the corners into the right position.
I use the layer method with a "notch", where one corner is left unsolved until the very end and you flip peices in and out of the notch in order to put them in the right place. I'll look for a link that describes it and post it if I find one....