Buzzing the mouthpiece is the basic exercise to get a sound out of a brass instrument. Getting the mouthpiece to buzz can be easy or difficult, depending on the type of instrument--a tuba doesn't take much to get a sound, while a trumpet is more difficult. Once a player has this basic technique down, they can begin to perfect and adjust their embouchure to play the various notes on the scale.
Chances are that everybody has buzzed their lips in their life. Think of children mimicking the sounds of motorboats. Begin by practicing without the mouthpiece. Blow through your mouth, with your teeth and throat open, without puffing your cheeks. Push the air with your throat muscles. If all you hear is air, put your lips a little closer together while keeping the same amount of space in the center of your mouth. Practice mouth buzzing for long periods to generate a steady buzz.
When you are able to get your lips buzzing, try putting them to the mouthpiece. But before you start blowing, practice your embouchure--the way a player places the mouthpiece to their lips. Holding the mouthpiece near the end of its shank, bring the mouthpiece to the center of your mouth, making about 2/3 cover your top lip. Make sure that the mouthpiece feels comfortable against your lips. Begin buzzing your lips. Apply as little pressure as possible, so as to avoid lip damage. Keep blowing and try to develop a clear, consistent tone.