The U.S. Supreme Court is the highest court in the United States. Every year, hundreds of appeals are filed there and only a few end up being heard. I know a very bright and accomplished attorney here in Richmond who told me he was very nervous when he argued there. The Justices of the U.S. Supreme Court have become known for the way they question or don't question attorneys during arguments. Justice Thomas is known for having gone eight years without asking a question of an attorney arguing before the U.S. Supreme Court.
The U.S. Supreme Court has a relatively small gallery and the arguments are not broadcast or streamed live. The U.S. Supreme Court blog has begun posting audio files of arguments in a project called The Oyez Project. The name Oyez comes from the traditional opening greeting when a court comes to order following Oyez being said three times.
Through The Oyez Project you can give a listen and put yourself in the shoes of the select lawyers who argue before the U.S. Supreme Court.