Oral argument is where a panel tests the positions it has formed from the briefs. Preparation should assume the judges have read them.
Open with the point. One or two sentences stating what the court should hold and the strongest reason. Panels interrupt early, and an argument that saves its best point for the end may never reach it.
Answer the question asked. Directly, first, then explain. Deflection is noticed immediately, and answering a hypothetical with a statement that it is not this case is the least effective response available.
Concede what must be conceded. A candid concession on a subsidiary point purchases credibility on the central one, and refusing to concede anything signals that nothing said can be relied on.
Know the record cold. Page and line for the key testimony, the exact wording of the disputed clause, and the procedural history including dates.
Know the consequences. Judges routinely ask what rule the court would be adopting and how it applies to other cases. Have an answer that is narrower than the broadest version of your position.
Rebuttal should be short and address one or two points actually made, not a prepared summary.
Afterwards. Supplemental authority letters are for genuinely new authority, briefly, without reargument.