Being prepared is the key. I've done a lot of public speaking/appearing before a panel type things, and if you are confident and have thought everything through, the preparedness overshadows the nerves and you'll do fine. Now, as to whether you'll have time to adequately prepare, that's another story...
I have TONS of public speaking experience, although not in a legal context. Preparedness is key. Also, if you can have a friend or several friends or family members act as audience members it will help. Try to listen for irritating bad speaking habits, like saying "um" or "ah" when you are thinking of the next thing to say. Not doing those verbal fillers will make you sound much more polished even if you are not.Be mindful of your body language. Stand in front of a mirror and go over some body language. Think of how you stand, where you put your hands. Suddenly in front of an audience it will be tough to remember what to do with your hands!Make eye contact as much as possible. Not only will it engage your audience, but it will get to you lose reliance on reading your notes and make you seem like you know it cold (which you should).Speak slower than you think you should. When you are nervous, the adrenaline will make everything SEEM slow, but to your calm audience members you will sound like an auctionier.I don't know if this is appropriate in a legal presentation context, but make eye contact and smile within the first 3-5 seconds. Smile fully, showing your teeth, or it will look fake and sarcastic. I would think in most public speaking contexts, even if you can pull off a quick flash of a smile at your audience and a "Thank you" (for inviting you to speak, for the intro, for calling you up, etc) could make you seem warm and genuine, relaxed and confident, even if after that you turn serious and make a very professional presentation.That's all I got for general public speaking tips.
Agree with everything except the smiling part. Though it may be appropriate in most other contexts, in the context of moot court (where you are usually dealing with a case involving someone who's been seriously hurt or egregiously wronged in some way), it'll often just make you look goofy or flippant. People are in court because they're unhappy and upset; the overall mood is a very formal and serious one. The ones who should be responsible for lightening the mood with humor, etc, are the judges; take your cues from them, and follow their lead. If they are smiling, then smile, but I'd say it's probably best not to do so on your own initiative.
So during our first year of law school, I'm sure we'll all have that "oh crap" moment when we realize we will have to start doing oral arguments for professors and judges soon (at my school, you have to do an oral argument before a panel of judges as part of legal writing).