Not only is the screen the window you view the iPhone interface through, it is the interface.
That being the case, the iPhone screen gets dirty quickly and easily.
To clean your iPhone’s screen, NEVER use any type of cleaning solvent such as Windex or other chemical agents.
Use only water.
Use water and a lint free, scratch resistant cloth (microfiber preferred) to clean your iPhone screen by dampening the cloth slightly and clean the screen using soft, even strokes.
The 3M Microfiber Cleaning Cloth, available in the iPhone stores, is highly recommended.