Here's a book you might find useful in order to prepare: Supreme Court Practice, Ninth Edition.
For guidance on every aspect of practicing before the Supreme Court, rely on this trusted source of the Justices’ law clerks for over 50 years.
Rely on this treatise for guidance on every aspect of practice before the Supreme Court—from how to pass through the guarded entrance to get to the Clerk’s Office, to whether to file one or more petitions in consolidated or related cases. Supreme Court Practice, Ninth Edition is the definitive resource for everything you need to know to prosecute or defend a case before the Supreme Court. This treatise provides:
And it seem to be a bargain at a mere $455.