Keep your letter to one page if possible. Put your address on the letter Envelopes and letters get separated, so be sure your address is on your letter as well as on your envelope. If you want a big, signed picture, send an eight and a half by ten envelope with postage on it and your address. You can almost always reach somebody famous through the place they work for. Bands have record labels.
Writers have publishers.
Athletes play for a particular team. Look on the jacket of the CD, the box of the video or the inner page of a book. Official websites are also a good place to find addresses. You can find lots of listings by typing in the name of your favorite star at the Yahooligans website. Here are a few addresses I dug up for you from different places.