Anytime you take your dog to a public dog park there is risk involved. It can be a real fun place for you and your animal companion, but can turn quickly into a scary place if a fight breaks out. The safest place for your dog to exercise and socialize is a doggie daycare where they have skilled and trained staff to place dogs together that are the right size and temperament with each other. It is a controlled environment that lessens the chance of a dog scuffle, not to say it can't/won't happen but the chances go way down when you have people who know dog body language supervising the dogs.
With that being said if you do choose to use the dog parks that are available there are some things you must know, some dos and don'ts
Do be Aware
If there is a dog that looks like trouble and the owner is not supervising, probably best to stay out of the dog park.
Do bring poop bags
So many times the parks will run out and you don't want to be that owner who doesn't clean up after their dog. Dog feces can spread disease and it's not pleasant to step in.
Make sure your dog has plenty of access to water
Especially on hotter days. The park may have a fountain but may not always work so have a backup bottle and bowl in your car.
Research and study dog body language online
This is the primary way a dog communicates and most fights can be prevented if you know what to look for. I.E. a tail wagging doesn't necessarily mean "I'm friendly and want to play" educate yourself to help protect your furry friend.
Take off all collars except buckle type (choke, prong, etc.)
Anything loose can get caught easily on a dogs paw when two are wrestling. It can inevitably start a fight if one dog gets attached to another is in pain and can't get away.
Be cautious of taking advice from other dog patrons who are not professionals.
Bring food or treats of any kind
If dogs smell them on you they will swarm you like a hive of bees and your dog may try to protect them. This is one of the easiest ways to start a scuffle.
Don't get distracted
You are there to supervise your dog as well as learn by watching them with different sizes and temperaments of dogs. If you know your dog's body language and he/she shows signs of distress you can possibly prevent a problem from happening.
Your dog should not be allowed to bully another dog
If a dog is bullying your dog stop it immediately and make sure owner is aware.
Make sure your dog responds to verbal commands
Have some sort of training under your belt prior.
Don't bring puppies 4 mo or under and are not fully vaccinated
Along that line do not bring intact males or unneutered females into the pack. Your intact dog may be perfectly well behaved but it's not them you need to worry about as much as how the other dogs will react to them. Intact males have a surge of testosterone pumping through them and other dogs can take offense to them for that reason solely which could start a fight. You never know when a female will go into heat and you don't need any oops mistakes or other dogs swarming her.
Don't worry if your dog doesn't play with every dog
If they show signs of stress - heavy panting without exercise, shaking, hiding behind you, etc....its best to remove them and contact a trainer. If their stress level gets too high or goes ignored they may act out if another dog approaches innocently to smell or greet.