1. Be courteous, respectful, and treat the dog park like your own yard.
Dogs parks are generally maintained by a non-profit group of loving dog owners; even if the dog park is "city owned," funding and care often comes from volunteer contributions. They have been gracious enough to volunteer their time for your dog's enjoyment.
2. Read the Dog Park rules before entering.
Just because something is acceptable at home doesn't mean it is okay where you are visiting. When in Rome do as the Romans.
3. Be mindful of all canine citizens.
Just like people, dogs have unique personalities, likes, and dislikes. Just like some people unintentionally annoy us, some dog personalities aren't compatible. Do not let your dog be an annoyance. Be a responsible doggy parent as necessary -- just like you may not think all human kids are cute, chances are not everyone thinks your canine child is cute either.