Dogs generally handle chemotherapy drugs much better than humans do. While they may experience some symptoms, they are usually not as severe as one that you would see in a human being. Some of the most common side effects are hair thinning, skin irritations, swelling, nausea and hand tremors.
Your dog might also get diarrhea two to five days after the administration. Dogs usually don't have the severe symptoms, but you should call the vet if you see anything that seems unusual.