All great suggestions above, if I may offer a few additions:
Have a good meal beforehand, nothing too heavy, to keep your energy up without making you feel bottom-heavy. Stay hydrated and bring a towel (+1 Cerna), the energy of the room plus the perfectly natural first-gig jitters may mean a lot of sweating.
If the person in charge hasn't prescribed a format or genre for your set then be open to requests of all but the most ridiculous nature. My first gig as a house DJ I really wanted to play MY style of house and I struggled with people wanting bouncier (ie NRG) dance music the whole night.
Definitely do a bit of pre-planning on your first time out. Pick an opener, a closer, and some good 2 or 3 track combinations that will work in the body of your set. Practice coming in and out of unfamiliar music at home into more familiar ground, to simulate mixing out of that request you could not refuse.
Finally, smile. If you at least look like you're having fun back there others will reflect that energy on the dancefloor. Have fun, good or bad it'll be over before you know it, and there will be lessons to learn but the first free minute after the last bit of gear is zipped up lean back and bask in the achievement, the first gig is a milestone for sure.
Break a leg out there.
1. Be prepared when it comes to knowing the type of music the people will be expecting.
2. Don't get shitfaced before you go on.
3. Don't get too caught up in trying to correct mistakes when it comes to mixing.
4. Pay attention to the crowd. If a tune is working really well, try and build off that with similar tunes.
The worst mistakes IMO, are doing the opposite of the above: -
1. Not knowing the crowd and/or trying to "educate" them with shit they don't want to hear.
2. Getting shitfaced which affects not only your ability to mix, but your judgement.
3. Fucking about trying to fix trainwrecks that only prolongs the agony.
4. Not paying attention to what people are feeling musically.
If it's anything like my first gig, you will feel a mix of nervousness/excitement, but after a few minutes of mixing, the nervousness will be pretty much gone and you'll be buzzing.