The Mori program is an attempt to classify algebraic varieties (over C) with respect to biregular or (more realistically) birational equivalence. While some key pieces are still conjectural, the program aims to identify a good representative in each birational equivalence class, and to provide an algorithm for finding this representative. I will introduce the basic techniques of the field, beginning with the case of surfaces, and then address the difficulties that arise in higher dimensions via concrete examples.