And just because a judge asks you a question, don't assume it's unfriendly or hostile. Sometimes, just sometimes, judges ask "softball" questions to help the attorney convince the rest of the panel. Be on the lookout for these "softballs" and if you get one, use it to your advantage.
If you don't understand a judge's question, ask for a clarification.
If one judge asks you a question and before you can complete an answer another judge shoots you another question totally unrelated to the first, look to the justice presiding for direction. It may not be a good idea to get into the cross fire of two judges.
If a judge has asked you a particularly probing question and you have answered it, don't be afraid to ask the judge if your answer is satisfactory. By the way, this is probably the only time it's ok to ask a judge a question.
If you have the time and the means to videotape your preparation, do so. You may learn a lot about how you appear to a group of judges. It would be ideal if some of that video preparation included some questions thrown at you by friends or colleagues.
I read the reply brief first and work backward. The reply brief shouldn't be a regurgitation of the brief-in-chief. It should be a finely-honed piece of writing dissecting the respondent's points and reasserting the principal points of the brief-in-chief. As a respondent, anticipate this and proceed accordingly. Perhaps you might want to conclude, "Appellant, who gets the last word, will probably tell you (the following). But, that cannot be the case for the following reasons:"
Finally, in most cases, oral argument probably doesn't matter that much. But, in those close cases, it may very well be the difference between winning and losing.
David B. Saxe is an associate justice on the Appellate Division, First Department.