I figured out how to solve the Rubik's cube by myself, and I can tell you from my experience that I found it much more rewarding than by looking up the solution in some book or at www.rubik.com, where a nice graphical how-to is provided. (as a side note, the solution at www.rubik.com is the same as in the entry by alex.tan, and both of these are very similar to my solution as well) I suggest you also figure out how to do it on your own, but provide this crude outline so that you have half an idea of what you're supposed to be doing:

Step 1: Solve the top side completely, so that the center pieces of each of the sides match the sides of the top layer
Step 2: Solve the middle row (yes, with a little work, you can figure it out on your own).
Step 3: Finally, break off the remaining bottom-layer pieces and replace them in their proper positions.

The added bonus of this method is that if you work on your Rubik's cube in public, people will see you fiddling around with it for a few days or weeks, and so when you finally have it finished, they will think you are a genius for having solved it on your own. Plus, you won't waste countless months trying completely in vain to figure out the bottom layer, as I did.