I'm sure many of you are aware that many games use a 2x2 set of squares to create a single tile. For example, the graphics of the Goomba enemy from the original Super Mario Brothers is made up of 4 squares, like this:

Well, my main problem is dealing with the tiles that you normally use for the world map in SMB3. There are so many shared squares that changing a tile usually changes another. I want to be able to change which of these graphic squares make up a tile so that I can modify things more freely. Unfortunately, I have no idea how to do this.
Is there someone out there that knows how to do this? If so, could you bring me through an example?