Calculating Avogadro's Number
Placing a drop of oleic acid on the surface of water contained in a pan is a relatively straightforward experiment that has been widely used to determine Avogadro's number.  Here are two links that provide good background on a) how to run the experiment, b) how to analyze the data, and 3) the science behind the experiment.  The two links are just variations on the same experiment, but if you read them both it will really enhance your understanding of the experiment. 

link 1

link 2