Many different methods exist for solving the cube.

Originally, I employed the classic layer-by-layer (LBL) solution.  For my earliest solves, I actually used commutators to cycle edges into the middle layer.  I quickly switched to the so-called "keyhole" method, in which a free corner in the top layer is used to slot in the equator edges.  This method allowed me to win 1st place in my first competition.

Soon thereafter, I purchased Minh Thai's The Winning Solution and decided to try his method.  Within a few months, my times had dropped to an average of 33 seconds.

Coming soon:  Details on the variation of Minh Thai that I used.

Meanwhile, check out these downloadable PDF files for some good solutions:

Leyan Lo's Beginner Solution
Jasmine's Beginner Solution