Hello again and thanks for waiting.
I have worked out an answer for you, please read it through and see what you think ...
The bottom line is that this sort of thing is always a gamble so if you want to be 100% sure you are doing the right thing you should have a vet check your dog over without delay.
That said that there are a number of home remedies for vomiting in the dog which some owners use while waiting for their vet's appointment. These very often work well work well for uncomplicated cases where for example a dog has eaten something he should not have out in the yard, or some unaccustomed rich foodstuff, or has a minor tummy bug. Here are some examples.
1. I am aware that some owners use Pepto-Bismol to treat their dogs with gastro-enteritis and report success. Here is a link to a web page which has all the information you might need including dose rates : LINK
2. Some owners try and control the situation with diet alone before they try anything else. This is logical and often works, the basis of this is to give the intestinal tract a complete rest and then bring it back slowly to function, resting the alimentary tract is the critical factor. It would go something like this ...
A. Starve him for 24 hours but make sure he has access to water.
B. The next day feed him four or five small light meals in the day. These meals should be the likes of chicken, fish, scrambled egg etc. with a little rice.
C. If he picks up on this diet gradually reintroduce his normal diet over the next few days.
3. Live yogurt added to the food can often help. Some gastro-enteritis situations are caused by an imbalance in the bacteria in your dog's gut. Live yogurt is full of " good " bacteria and will seed them into your dog's intestinal tract and restore the balance. You do not need to give much, perhaps a couple of table spoons twice a day.
Of course if any of the above does not quickly start to work or if your dog deteriorates further in any way you should see your vet without delay just to be on the safe side.
I hope I have given you a few ideas and covered your question fully enough but if you would like further clarification or to talk things over a bit more then I will be on-line for the next hour or so and I will be more than pleased to continue working with you.