Congrats. My advice is this: certainly do have fun playing; however, also remember that you're there to work (you've been hired), so there are some do's and don't's that often go with the turf:
Do: Like Jason Oldsted suggested and show up early for set-up and for plenty of time to take care of any pre-gig emergencies ("I thought YOU were bringing the PA head!")
Do: Bring plenty of extension cords, power strips, duct tape, 9 volt batteries, extra strings, fuses (for your gear), and some first aid goodies like aspirin and something for a wacked-out stomach.
Do: Bring a roll of plastic if it's an outdoor gig so you can quickly cover your stuff if it rains, or yourselves if the crowd gets wired and starts squirting you with beer.
Do: Make sure you and the host have agreed on the exact start and end times, keeping in mind that most towns have curfews when it comes to outdoor noise...or noise that shakes through walls.
Do: Specify how you should load in and load out. There's usually hell to pay if the band tramples the flower garden into a mass of compost.
Do: Specify up front the amount that you're getting paid and that you want to be paid in cash (don't make a scene if you get a check).
Do: Ask the host where the bathroom is when you first get there, and make sure the drummer doesn't use the shrubs.
Do: Have your set list ready to go and planned for the X-number of hours you'll be playing, with breaks accounted for in between. Also, have some extra tunes available in case you get asked to play longer.
Do: Not be afraid to ask for more $$$ if you're asked to play longer than the agreed-upon time..unless it's a biker party. In that case, just do whatever they ask and don't ask any questions.
Do: Whatever the host asks regarding volume (i.e., turning down). If it gets to be a hassle 'cause the neighbors are calling the cops, suggest to the host that you call it a night and ask to be paid for the time that you've played.
Don't: Bring your "significant others"...unless they've been invited by whoever hired you.
Don't: Mingle with the party crowd. You're the hired help and are not there to socialize (unless friends have hired you to play). It's okay if a party guest comes up to you to talk...who knows, he/she might want to book a gig with you or ask you out.
Don't: Assume that you can indulge in food and beverages unless the host has said it's okay.
Don't: Let the drummer near the bar or the food table unless accompanied by another band member.
Don't: Take long breaks between sets, and don't let the drummer wander off too far.
Don't: Dawdle at the end of the night (unless you're friends with the host). Pack up your stuff quickly and quietly and go home or to a bar to celebrate your first gig, but don't blow the whole wad of cash that you just earned...save some of it for that future recording project.
Don't: Laugh or make rude remarks to a guest who requests a song that you wouldn't be caught dead playing. Be nice and tell them that you'll try to learn it so you can play it for them at the next party (this is called "Lying Through Your Teeth For The Sake Of Your Art").
Don't: Hit on the host's boyfriend or girlfriend (whichever is applicable).
Hope some of this helps.
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Been there, done that, can't remember most of it...except the low parts.
