While working on your dog, I am increasing blood circulation and getting nutrients back to the muscles. It is expected that their nose might start running (and they might sneeze), they might begin panting due to warming up the muscles in the body, and they likely will start closing their eyes. Dogs often help release tension through stretching and yawning when working out tense muscles or knots.
Your dog will most likely need to relieve themselves or want a drink of water immediately after a massage. A nice shake or stretch after treatment always shows they enjoyed the bodywork. Monitoring their gait as they walk away will also show how balanced they are.
When you get home, keep an eye on your dog. It is common for them to be tired and sleep, especially after their first session. On the other hand, some dogs react oppositely and are highly energized, playing when they otherwise wouldn't be! If it is your dog's first massage and you don't know how they will react, I would not recommend asking them to do any dog sports after a massage.