If your dog eats grapes and it makes them sick then you should start noticing the symptoms within 24 hours of the dog ingesting the grapes.
Not all dogs will get sick from eating one or 1 grapes though and usually it takes more than a few grapes to actually make the dog sick.
My dog got into a few grapes and I called the vet and they said to just keep an eye on the dog and if it was gonna affect the dog it would within 24 hours and if so to bring the dog into the vet.
The dog was just fine and never got sick but I don't feed the dog grapes but sometimes they get into them without me knowing about it or by the time I catch them it's too late.
If the dog does get sick from the grapes they will experience symptoms such as vomiting, loss of appetite, diarrhea and pain in the abdomen.