Here's a few thoughts -
First thing - Have fun! Waterskiing is a competitive sport but it's important to remember everyone is there because they truly enjoy the sport so enjoy yourself and have fun! Getting involved is a great way to learn what's going on and support the sport.
When you get onsite look for someone registering skiers. You'll need to fill out an entry, sign a release and pay an entry fee (all of which may have been sent in or filled in online but you should check in anyway). You'll need to be a member of USAWS so be prepared to show your membership card or you can sign up on site.
The competition is primarily aged based so you'll be in a group with others close to your same age (Page 7 here - http://www.usawaterski.org/pages/divisions/3event/2012AWSARuleBook.pdf). Tournament organizers can mix up groups in lots of different ways so look for a running order to determine when you ski.
Take a few minutes to read through the rules for slalom (same link above starting at Page 41. Go to other sections for Jump and/or Tricks). We all know what a slalom course looks like and some of the rules may not apply to all the tournaments but it's a good idea to understand what the judges are looking for and how your performance will be scored.
The suggestions above to see if there's a grassroots division is a good one. The division is perfect for newcomers and offers a little more flexibility meant to help flatten the learning curve and keeping things fun. Most times you'll essentially get a potential mulligan if, for example, you don't make your first pass, etc. Once you perform to a certain threshold (max speed @15off?) you'll need to ski in your age division from then on.
When it's close to your turn, get all your stuff together and head down to the starting dock. You'll get a sense of the pace of things pretty quick. Ask around to see who skis one or two people in front of you and keep an eye on when they head out to ski. Sometimes running orders are adjusted on the fly (non-seeded tournaments like typical local tournaments only) to accommodate officials so just go with the flow.
When your turn arrives, be ready to ski when the boat gets back to the dock. If you have your own handle pass it to the boat crew. Tell them your starting speed and rope length and perferred ZO setting. Some folks like to chat a lot others are pretty quiet but generally the skier sets the tone so if talking to the boat crew at the end of the lake helps, go for it. Here's a good primer on possible subject matter -
When you ski, expect a good pull. Drivers and judges are there to make the competition fair and enjoyable for everyone and the goal is to follow the rules. When you fall don't expect the boat to come pick you up, usually we swim to shore and start the long walk back to the starting dock. Pay attention to where most folks walk back, nothing's more miserable than having to walk back on the "wrong" side of the lake! If you have a hard fall and assuming you're alright, wave to let everyone you're fine since there are folks responsible for safety looking for some indication.
Since most tournaments are multi-round, it's basically - lather, rinse and repeat! While you're waiting for your turn, get involved! Tournaments everywhere are run by volunteers. Scorers, judges, drivers, safety, tech controllers, etc. are generally skiers doing what it takes to make things work. Every tournament has a chief judge, chief scorer and chief driver. Each slalom pass has a driver, scorer, and three judges (or 5) determining your score and recording it. If judging or scoring sounds interesting, ask the chief judge/scorer if you can help. They'll put you with another scorer or judge to 'shadow' what's going on and they will be more than happy to walk you through the responsibilitiies. If driving is more your thing, ask. Beginning drivers help with moving boats around, refueling, etc. but certainly a chance to ride in the boat for a group or two will give you a good idea of how things work. For any of these officials positions there are simple 1-2 page forms which get filled out to record your 'work' history. Once complete you can aspire to a higher level. Getting involved (and/or other skiing and non-skiing friends and family!) keeps things interesting and really does make a difference running the tournament.
Finally, again, have fun! Don't expect to set a record at your first tournament but DO expect to meet some great people eager to get you involved and always happy to share their passion for a sport we all love.
Good luck this weekend and let us all know how it goes!!! By the way, look up @Dirt while you're there.