I'm coming at this article with a two-pronged approach because I want to share a gentle way to teach a pup to sit, and I also wanted to share a key way you can be clearer with your dog—marking behavior.
The core idea of a reward-based training program is based on a basic fact of canine—and human, but we'll get into that later—psychology. Dogs do what they practice, and they do what's rewarding. The more times a dog repeats a behavior, the more likely he is to do it in the future, and the more the behavior is rewarded, the more likely he is to choose it in the future. Much of my training is based on this principle, but this article focuses in on how to reward effectively and precisely, and it does so in the context of teaching your puppy sit.
The first principle of rewarding is that the dog determines what's rewarding, not the person. You can't force your dog to like something he doesn't like. With that in mind, I often use food as a reward, but it cannot be the only tool in your training repertoire. Some dogs don't care that much about treats, and some that do still won't take one when they're excited. If you find yourself begging your dog to take a treat, it's not a reward. So keep in mind that even though I'll describe the sit with a treat as the reward, you can use a toy, a game, or praise as a reward as well—whatever motivates your dog. Good trainers are creative and diverse with their rewards.
The second principle of rewarding is marking the moment of successful behavior precisely so your dog knows exactly what behavior led to the reward. In methods that incorporate the clicker, the clicking noise marks the behavior. That works wonderfully and has a number of advantages. But you can accomplish nearly the same thing by saying, "yes!" in gentle, positive tone. The key is that you use your marker at exactly the moment the dog does the thing that will lead to the reward. For the sit, that means saying "yes!" right as the rear end touches the floor.
Remember: success is going to be more about your clarity as a handler than about your puppy's personality or intelligence. To that end, remember these principles: don't say commands your puppy doesn't know, mark the moment of success, and follow a mark with a reward.
Hold a treat in your fingers and show it to your pup. Then as his nose is focused on the treat, move the treat upwards above the puppy's eye level and move it toward him a little. As his head comes up and back to follow the treat, his rear end should lower to the floor. Mark the moment of success by saying "yes!" Then follow the marker immediately with a reward. If you were luring with a treat, be sure to give the treat as part of the reward.
You may have to practice a little in order to figure out the hand motion that will get the pup to sit reliably. That's OK, and it's one of the reasons you shouldn't be saying your puppy's name or "sit" yet. However, it will help if you start at the puppy's eye level and then bring your hand up a few inches, because that will translate nicely to a hand gesture once you fade the lure away and stop showing your puppy a treat.
Remember to say "yes!" at the moment the puppy hits the sit position. Make sure his rear is in full contact with the floor—so you're not teaching the puppy to half-sit. Timing your marker is actually a bit challenging when you're first starting out, but stick with it. If you are fun and generous, your puppy will bear with you and you'll get the hang of it.
Once your pup is consistently sitting when he sees the lure and gesture, you can start saying "sit" as you make the hand motion. If your rewarding is generous and your marking is precise, you should progress fairly quickly together.
The last piece of the puzzle is fading the lure. The biggest pitfall with food lures is that they can turn into bribes if you don't fade them early enough in the process. You don't want to teach your puppy to evaluate what you have in your hand and compare it to whether it's worth it to obey. If you get in the habit of showing your puppy a treat and then asking for compliance, you'll end up in situations where you either don't have a treat or where the treat simply isn't motivating enough.
So once you're seeing a reliable behavior that uses the lure, the mark, and the reward, take the lure out. Do the command exactly as before, except this time, don't hold a treat in your fingers. Hide it in your other hand, behind your back. If you've repeated the behavior enough times, and you change as little as possible besides the location of the treat, your puppy should sit like normal. Then, mark the moment of success and bring the treat around from behind you.
I've described all of this as if it takes place in one session, but you'll have more fun with your pup if you make sessions brief and frequent and only take one step forward every few days. Spend 3-5 minutes a couple of times a day on "sit" and your pup could have it in a week or less. Keep sessions short and light-hearted, and always end while your pup is still having fun. Puppies have short attention spans, and you'll lay really good groundwork for long-term fun training together if your sessions always end with the pup wanting more, rather than ending with your begging the puppy to pay attention.