A moot is supposed to simulate an appellate hearing. In real life, the advocate's role on an appeal is mainly to answer the questions of the Court, but you should prepare submissions before the moot.
Try to have no more than five points. Star advocates such as Lord Pannick KC rarely have more than three points. Start by telling the Court the outline of your submissions: "My Lords, I have three points. They are 1..." (etc). Then do the first point.
When asked a question listen carefully and answer as clearly as you can. Do not speak over the Judge.
When moving on, say "That was my first point. I turn to my second point...".
If referring to a case, cite at most the headnote (if the Court wishes), and the key passages you rely on. Deal with any authorities that are against you and explain why the case can be distinguished or was wrongly decided (assuming that the simulated court you are in is the top court).
After you finish, listen carefully to your opponent's submissions. When replying, focus only on the most important points, and be brief.
Watch online videos of the Supreme Court, especially cases featuring Sir James Eady KC, Dinah Rose KC, and Lord Pannick KC, to get an idea of how it's done. There are also some videos online of Pushpinder Saini KC (now Mr Justice Saini) in the ECtHR. Push is another masterful advocate.
Have fun, good luck!