Remember that it is also a place for recreation by people who don't bring animals. To some of these people your dog's presence could be seen as a nuisance if they don't behave themselves properly. If you or your dog are inconsiderate people may complain and you could be asked to leave the park.
When playing in a park for dogs, make sure to obey all of the rules posted in the area. If off-leash play is allowed only during certain hours, leave your dog leashed according to the posted times. Hour restrictions are usually for the safety of others during crowded periods during the day. If the park has written rules about which areas dogs may be off-leash, and which areas that leashes are required, always be ready to leash your dog again according to the rules.
You should always clean up after your dog. Failure to clean up after your dog is among the highest reasons that a dog park changes signs to read no pets allowed. Dog waste left uncleaned makes an area unsafe to play in and contaminates ground water sources once it decays. If dog waste is left behind people will step in it and children may fall in it while playing. You wouldn't want to have some kid's skinned knee landing in a mess left behind by your dog. Cleaning up after your pet is not just polite; it's a matter of safety for people and other dogs.
Everyone's dog has a favorite toy but these toys should not be brought to the dog park. If you do bring a toy to the park every other dog there may end up wanting that toy as well. While your intentions are good, this can also cause some issues. You don't know how other dogs will react and toys can cause serious and potentially dangerous fights to break out in the park.
Everyone knows it's your responsibility to clean up after your dog, but only a few realize that part of minding your manners also means keeping your dog clean and dry. Be prepared with a couple of towels to wipe your dog down. If your dog goes for a swim make sure you dry it off before it shakes water all over an innocent bystander. If your dog is soaked in mud, wipe her feet before you return to the paved path. People who don't bring their pets with them will be judging you, and your dog, so keeping him clean is a good way to ensure that everyone gets on well.