You can recognize signs of illness in your pet by observing changes in their behavior, appetite, energy level, and physical appearance. Some common signs of illness include lethargy, loss of appetite, vomiting, diarrhea, coughing, sneezing, excessive thirst, and changes in grooming habits. If you notice any of these signs or any other unusual symptoms, it's best to consult with a veterinarian for a proper diagnosis and treatment.