Great. Thanks for the additional information. I really appreciate it.
Because this has only been going on for a very short amount of time, and since from your answers, we can rule out things like ingestion of a toxin, intestinal obstruction due to eating something non-food, and pancreatitis from eating greasy people food, I think we should just treat it like a case of simple digestive upset.
The gold standard for treatment of digestive upset in a dog is fasting. Generally the problem is acute (meaning it comes on quickly) and can be taken care of without much trouble.
If this were my dog, I'd fast him for 24 hours (providing he doesn't have any underlying diseases such as diabetes that require he eat every few hours). No treats, no food, nothing. You can leave a small amount of water available, but don't allow him to drink too much at one time (placing ice cubes in his bowl so that he can't gulp water will help).
After the 24 hours, I'd offer a bland diet of boiled rice and boiled hamburger (3 parts rice to 1 part burger) in VERY small amounts (perhaps 1-2 tablespoons every hour or so) for the next 24 hours. Once you start feeding the rice mixture, monitor the dog for recurring vomiting. If the problem doesn't start again, you can begin slowly mix in his kibble over the next few days until you're back to just kibble.
If the digestive upset persists for more than another day or so, or if your dog becomes lethargic, begins to have blood in the vomit, starts having bloody diarrhea or shows other 'unusual' signs, you should have him seen by a vet, just to rule out any sort of illness or parasite infection, but as a general rule, this clears up with just the fasting and then bland diet.
I hope this helps.