Your dog is probably vomiting because it has eaten something that is not agreeing with it's stomach, and the lethargy is because the vomiting is making it dehydrated.
You need to starve the dog for twenty four hours. This gives the dog enough time to pass whatever is causing the vomiting. Since vomiting can make a dog dehydrated, make sure you keep the dog well hydrated by giving it water. After twenty four hours, you should give the do a simple meal of chicken and boiled rice as this is easy to digest.
If the vomiting starts again, go to the vet as it could be something much more serious like a toxic substance that the dog has swallowed. Make sure you keep the dog well hydrated till you are able to take it to the vet.
