I have a question for you before I can begin to answer this question. How old is this dog and has he/she been fully vaccinated against Parvo, Carona Virus, and the like (the usually boosters they get as pups before they get their first rabies shot)?
For starters, you need to try to get him/her to keep fluids down. I recommend boiling some chicken, and letting the broth cool, and giving via syringe if you can't get him/her to lap it up on their own. Keep the dog separate from the other dog until you can determine what's wrong. Reason being, if he/she has contracted Parvo, it will spread to your other dog and make that dog sick as well. Begin cleaning everything in your house/yard with a bleach/water solution, and washing your hands thoroughly after dealing with the sick dog, prior to dealing with the other dog or anything else in your house/yard. You'll also want to boil up some rice and try to get your sick dog to eat the rice, after it's cooled down. Don't add salt, pepper or butter to the rice while cooking it. You want to feed a bland food to help settle his/her stomach. The chicken you boiled to make the broth, you can add in to the rice to see if that entices him/her to eat.
Next thing to do, is to schedule a vet appointment ASAP to have him/her checked out. We on the forum are not veterinarians and cannot make a diagnosis over the internet. We can only offer some suggestions to help you out til you can get your dog to a vet.
I hope you can come back and answer my question and offer more information to better help us to help you. Best of luck and keep us posted.
How old is the pup? is it drinking can it hold down liquids? If it cant keep liquids down GO TO THE VET, dehydration can kick in fast and things can go from bad to worse in a very short time. Otherwise I completely agree with the post above and you can try the chicken and broth.