Place butter in a pot or pan over medium heat. Cook, stirring constantly, until the butter becomes a very light brown. Remove from heat. Salted butter will brown faster. For info on brown butter, click here.
Place green beans in boiling salted water, and cook to desired "doneness." Drain and place immediately into ice water to stop the cooking process. Drain well. You could also use frozen beans, and cook them to your done stage.
Toss green beans with brown butter, salt, and pepper. Heat on warm if necessary.