Once your dog has learned the "sit" command and is sitting promptly most every time, you should begin to lengthen the amount of time that your dog can remain sitting. A fast sit is not of much use if he immediately jumps back onto all fours looking for something else to do. Your dog must understand that "sit" means "sit" and must remain sitting until he is released.
This is done by watching the dog closely once he sits. A dog’s body language will tell you a second or two in advance that he is thinking of breaking his sit. Once you learn what to look for, it is much easier to catch him before he actually commits himself to abandoning his sit. The signs are subtle, but usually are such things as the head turning from side to side, looking at or looking for something. The front feet often change position slightly. As the signs progress, you will notice the rear end beginning to "wiggle" around, signaling his intent to bring it up off the ground.
Keep in mind that a young dog or an untrained dog will almost always break a sit when someone approaches. It is right at this time, before your dog even gets up, and before the dog is showing those subtle, wiggling, antsy signals that he should be re-commanded to sit, in conjunction with either a low-level reminder on the remote trainer or a leash tug. This will interrupt your dog’s wayward thoughts of getting up and will cause him to look at you. Softly say "good dog", but remember that this praise should be enough to build his confidence that he is, indeed, doing what is pleasing to you, but not so much praise that he gets excited and jumps back onto all fours in celebration. Keeping the approaching person at a bit of a distance, or having them approach slowly will be helpful as the dog learns self control.
Gradually extend the amount of time your dog can sit and the distractions under which he will remain. Once you are seeing that your dog has just about maxed out his patience, be sure to give the release command of "free!!!" as a way of telling him that he is no longer under the command to stay seated. This eliminates confusion on the part of your dog. When he learns that "sit" means "sit" until he hears "free!!!", he will not be so likely to just get up whenever the urge strikes him or when he realizes that you’re no longer paying attention to whether he’s sitting or not. Make sure you teach your dog to remain attentive to command before you entrust him with being accountable for his actions when under distraction (either yours or his). During the formative, developmental training stages, you must remain focused on your dog while he learns.
Anticipating distracting situations and helping your dog to remain attentive to command is a skill that is learned. No "stay" command is needed when "sit" means "sit" every time, until released. It’s the KIS approach – Keep It Simple. Your dog will learn faster and you will see better, more reliable results.