The Oyez Project, run by Chicago-Kent School of Law, is a one-stop shop for Supreme Court oral arguments from the current term.
You can now listen to the oral arguments for the first big case of the term, McCutcheon v. Federal Election Commission.
To find other cases, click Cases from the bar at the top of the Oyez Project homepage. Simply find the case you’re looking for (they’re organized by date) and select the title. Once on the individual case’s page, click the link next to the audio button, and you’ll get an audio player to listen to the oral argument. A transcript of the argument will also play, including the picture of the person speaking so you can follow along. The case page also includes a brief set of facts and the issue before the Court.