Just remember it isn't all about power and loudness, whatever you intend to sing. It's about technique. If you have never used a vocal coach or had tuition then you don't even know yet what your voice can do. I guarantee, if they know their job and you can afford it then after 10 you should have a much better idea of what your voice can really do, or what you can do with your voice.
They will give you all the tips you need to prepare properly before you sing and you will probably spend your first lesson just learning them. But mbcl is right, don't hold back (not in power but in terms of expression). Ask questions, tell them what experiences or what you have noticed when you try to sing in a certain way for example. Don't be put off by being ask to sing something that maybe isn't to your taste. They have certain music that is tried and tested to see what you can do; to find your range and see where you are comfortable (now) and where you are not.
I can recall doing Barry Manilow extensively and finding a new level of respect for the guy!
If you think learning an instrument is fun but hard work, then working with your own body and voice is on a completely different level.
As regards tips, water is good but so is tea especially some of the recupertave teas like peppermint, camomile and so on. They often taste like sh** but they do have muscle relaxing properties ( I find).
As far as today is concerned I think you will learn what prep you need, but if you want to be ready to go then immediately before your appointment some breathing to clear the lungs and pipes (and head). In through the nose and out through the mouth. Normal but deeply for a minute and then for 1 minute staccato. 2 minutes concentrated breathing is quite a long time but it may relax you also.
Then a mouth excercise. I normally pretend my mouth is a wah wah pedal and wah wah away to a song I know all the words to. Believe me, after a 3 minute song of oral wah wahing you can get your chops pretty much around anything!
But as I say, you will probably get all this today anyway. I wouldn't suggest warming up your voice beforehand because you may overstretch and bugger it up before your lesson and they will assume you haven't anyway.
In your mind, afterwards, perhaps you think it is has been a crap experience, but don't be put off. Everybody can sing, good or bad, but those that go on to do it better will always garner respect. Standing alone on a stage, no instrument, just your own voice, joy, fear and power of expression, there is no hiding place. Take all of that.............that nakedness, sing, release your soul and move people.
Then form a death metal band and grunt for the next 10 years...............only joking!
Enjoy
Good luck. Singing
No Hits, No Hype.......................Classic Rock Jan 2012
