the solution method that's in the booklet that comes with the cube now is kind of annoying and hard. it requires memorizing something liek 7-10 algorithms (sequences of moves to perform specific tasks). with a little work and making more moves than really needed, this can be trimmed back to 5, which is what i first memorized. it was unsatisfying.
i found another solution online that requires only two algorithms, both of which have a great deal of symmetry and one of which was in the set of 5 i'd learned for the other method. in this method, you place all the edge pieces first with one algorithm, then all the corners with the other algorithm. both algorithms also have some sense to them and with not too much thought one can see why they work. the web site, however, was not entirely clear, so it took me about as long to learn this method as the other way. other people i've taught have picked this method up in about half the time of people i've taught the other way.