A lot depends on the breed and size of the dog really, but you will find the recommended dose stated on the packet (if in any doubt about the weight of your dog, either weigh him/her yourself or ask a vet to do it for you)
Basically don't give any more than the recommended dose. Side effects seem to be that either the dog is very drowsy or completely the other way and totally hyper.
There have been doggie deaths from Benadryl, but in fairness they did take quite a lot by accident. As with children, always keep medication out of the reach of pets too!
Here is a chart giving dog weight and recommended dosage, but if in doubt please ask a vet, too much of anything except love can kill a dog.