When it first came out I solved it from scratch and ignored the literature about it. I prefer to do problems and puzzles in this way because firstly it is much more fun and secondly, looking at other people's solutions first sometimes causes the mind to miss an interesting original line of thought. (Rather like music)
In the case of the cube, I began by searching for sequences of moves which leave all faces invariant except a small number, which are usually interchanged cyclically. A small collection of such sequences, fairly obviously, must solve the puzzle sooner or later (provided a solution exists, but we are told it does). Not being very bright, it took me three days to find such a set of cycles. Mine certainly wouldn't have been an optimal solution in any way !
After solving it, what you do depends on how deeply you want to go into it. It has a colossal permutation group. All sorts of intriguing questions and conjectures spring to mind and many volumes, treatises and computer programmes have been written about it.
Topic: Cube Frustration !