It does depend on the individual trainer.
The trainer I went to with Keeta does puppy classes, for young dogs. Covers watch-me (eye contact), basic position (sitting on the left with eye-contact), sit, down, recall on leash with prey attraction, recall on leash with a sit at front, and from front to the basic position., heeling on leash with eye contact. The heeling is practiced a lot. Stay is introduced, in the sit and in the down, but still on leash, with the handlers only moving away two or three steps. There are short periods of socialization at the end of each class, is small groups, supervised by the trainer or on of the assistants. Sometimes small adult dogs (terriers, etc, are in this class too in order to have dogs matched in size, and sometimes older, larger breed dogs that are very timid or fearful are included in the puppy class. Being the largest dog in class often gives them confidence.
Then there is a beginner big-dog class, for young to adult medium to large dogs. This is called Level I Obedience, same basics as above.
Level II is for graduates of Level I. Dogs of different sizes and ages are in level two. The classes are smaller as some off-leash work may be introduced. Precision and focus is stressed. Mild corrections are introduced. Stays, in the sit and the down, a la CKC/AKC obedience style,are practiced. Heeling past distractions (other dogs, trainer bouncing a ball, etc). Hand signals (that is fun to teach your dog), extended focused heeling. Move up, move back, move in to get your dog to adjust for a precise basic position.
This class also has an introduction to agility obstacles. Each class, we alternate between doing a few minutes of formal obedience, and a few minutes of working on obstacles.
We sometimes do fun tricks too, with Keeta's class, we trained our dogs to "go touch" - go and touch a point on the wall that we were pointing at, at chest level, so that the dog needs to stand up and touch with both front paws, and come back to us. This trick was so you could pretend that your dog was a movie police dog and you were sending him/her out to check out a building by looking in the window, and come back and report to you (Keeta did really well on this one, but I'm still waiting for her typed report, though - slacker!). Or in some classes, some other trick, like picking something up and carrying back (basically, a retrieve).
This is all this instructor offers - he also does tracking classes, which are also very popular.
From my readings on the 'net, and from my experience in a different class prior to taking his classes, he crams an awful lot of stuff in his classes, but it is fun to learn new stuff to practice at home. I had started out in some other obedience before going to him, but the pace was so slow, that I was bored to tears, and Keeta wansn't learning anything, because she wasn't being challenged.
With the other classes, I spent the same money and the same eight weeks working with my dog, and at the end, I had a completely different dog!