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We are able to break down the following four steps into at least two each, so that the memorization is minimal at the beginning.  However, each section will have a "Combined Step" that will complete the step in one set of moves (or in the case of Step Two, it will do the two sub-steps for each pair of pieces placed into the bottom two layers of the cube).

     This is the most widely used method, and I use it almost exclusively.  The cube is solved in layers, starting with the White side, and finishing with the Yellow side.  It averages around 57 moves per solve if you learn all of the move sequences for it!

Crane Photo Caption
Method #2) The Block, or "Petrus" Method

     This is another widely used method, but is not usually suited for the beginner.  If you are extremely fast at seeing and analyzing the cube, this might be what you are looking for.  However, since I do not use the method very much, I do not have all of the information you need to do this method quickly.  Its users often use this method to solve the cube in less than 50 (sometimes less than 40) moves per solve!  There is a trade-off, though: there is much more to memorize if you are going to use this method!

     This is actually the way I learned to solve the cube.  One of my friends from college taught me this way.  Being the obsessive freak I am, I learned Fridrich's layer method and ended up helping him learn it...It's funny how things turn on you!  This method is pretty easy, as far as memorization goes, but it can take more time.  I usually average about a minute per solve with this method (as opposed to about 27 seconds with Fridrich's method).  Hey...we all must start somewhere!

Method #4) The Corners-First Method

     This is a more experimental type of solve, but I only use it when I'm bored and want to spend more time per solve.  It begins with correctly placing the corners (thus making an X on each side), and then inserting the correct edge pieces into it.  This method also is very easy, but requires the most time out of all of my solve methods (except blindfold-solving).

     If someone came up to you and asked you to memorize the way a cube was scrambled, I'm sure you wouldn't know where to begin, but it is really not as complicated as it seems.  At first glance, you think, "nine stickers per side, six sides makes 54 stickers to memorize!"  However, we think of them as "Pieces," not "Stickers."  There are three rows, three columns, and three layers, making 27 pieces.  When you disregard the inside of the cube (which you never see), and the six center pieces (one per side of the cube--they never move position), there are only 20 pieces to remember, and they are broken into four steps:

          Flip edges to the correct orientation (knowing binary numbers helps!)
          Twist corners to the correct orientation
          Move corners to the correct location on the cube (1-8)
          Move edges to the correct location of the cube (A-L)