There are many examples, both from history and from the present day, of the law of supply in action.
Our first example can be one from history. This is the impact of the cotton gin. The cotton gin greatly increased the supply of cotton in the United States. The law of supply explains why. One of the major nonprice determinants of supply is the cost of producing a good or service. As the price of producing something goes down, producers will be willing and able to make more of it at a given price. That is what happened with cotton in the US. The invention of the cotton gin dramatically reduced the cost (in terms of time) that it took to produce cotton. With that, the supply of cotton soared.
Our second example is more recent. Another determinant of supply is the degree to which there are alternate things that suppliers can be doing. A recent example, of this is the supply of corn for food. Recently, the US government has subsidized the production of ethanol from corn. People who once supplied corn for food now had another option. More farmers started to sell corn to ethanol producers and the supply of corn for food dropped.
These are both examples of the law of supply in action.