There are many strategies for solving a Rubik's Cube, but there's one basic method most Cubers learn first.
With the cube facing you, make quarter-turn rotations until the same color squares appear in a cross or plus sign. Keep in mind that the center square is static. If the side you chose to solve first has a white center square, you'll want to line up other white squares to form a cross.
From here on out, it gets a little more complicated. After forming a white cross, seek out white corner pieces. To do this, you'll make a counterintuitive move: Put the top corner piece in the bottom row below its final destination. Then, move the row in this sequence: Ri, Di, R and D. Repeat this until the top corner pieces are in place and the first side of your Rubik's Cube is solved.
Flip the cube and place the solved side to the bottom. Your task is to make the edge pieces in the middle layer all the same color on the side that is now facing you. This will require a two-part mini-strategy. First, you'll perform U, R, Ui, Ri, Ui, Fi, U and F to create a vertical, same-color lineup in the middle of the cube. Second, you'll move Ui, Li, U, L, U, F, Ui and Fi to move all the edge pieces to the proper place. At this point, the bottom row and second row of your cube should be solved all the way around.
To solve the top and final row, you'll create a yellow cross using a protracted series of rotations. Keep in mind you may need to do this sequence several times to solve the final piece of the puzzle: R, U, Ri, U, R, U, U and Ri.
From there, it's just a matter of putting the yellow edges into place. If you have one edge that's solid yellow (all three yellow squares lined up), turn your cube to place the solved edge at the back. However, you may not have any yellow edges that are solved. In this case, you'll need to experiment to find out which direction is most effective. As you rotate, follow the sequence: U, R, Ui, Li, U, Ri, Ui and L. You'll need to repeat this two or four times to solve each corner, but before long, your Rubik's Cube will no longer be a mystery [source: Science Buddies, You Can Do the Cube].