This is one of the first things I learned when I took an interest in playing chess. It taught me the importance of controlling the center, developing pieces, and not letting greed rush my play. I believe this situation is a good one to learn early on. It comes up a lot in beginners' games, it gives you a solid understanding of why the fundamentals are actually "fundamentals," and gives you a trick up your sleeve for the unsuspecting opponent.
In the puzzle to the right, you're playing White. Your first move is to take Black's leading pawn with your Knight. Sounds crazy? Watch what happens. When you've solved it, use the arrow buttons to move back and read the move by move commentary.
Without further ado, I give you: Legall's Mate!