The first night, you'll probably be asked to come to class without your dog. You may be required to bring proof of shots, especially rabies (although many classes require a copy of this information with your advance payment). You'll undoubtedly be given a handout of what to bring with you to class and, even more important, what not to bring. Sometimes a specific type of collar and/or leash is required, but for most classes a regular (non-choke) collar and a regular (non-retractable) leash are fine. A jug of water and a water dish are good items to pack; a good instructor will give dogs water breaks frequently.
The first class with dogs will be chaos, at least at first. All the dogs will want to greet each other, and half of them will be overexcited. Dogs will be barking. Owners will be apologizing. Your dog will probably be the worst behaved one there (or it will seem that way to you). But you're there so your dog can learn to behave--no one expects him to know it all beforehand.
Don't feel like you've picked the wrong class. The instructor will get everyone settled and before long you'll be working on obedience--and those crazy dogs will calm down once they realize it's not just a social club.
Obedience class can be exciting and fun for dogs, but the first night it can also be stressful. It's a new situation and your dog may not understand what's expected of him. If you notice your dog yawning, that's a sign of tension. Your instructor will probably notice before you do, but if not, don't be shy about taking your dog aside for a quick break and some reassuring.