When you first visit a dog park, take your dog to an area of the park where no other dogs are around. While playing with your dog, observe what's going on around you. Do this for several days at the same time.
If you're lucky, you'll notice some regulars and their dogs. After you feel comfortable with what you've been observing, approach the regulars so your dog can play with the others.
If you don't like what you see, you might try another time of the day. You may find a group of regulars and their dogs that you like at this time.
Practice frequent recalls with your dog at the park. Stay vigilant. As soon as you see or hear something that doesn't seem right, recall your dog.
Walk your dog away from any other dog playing with balls, frisbees, or other toys - even sticks.
If you want to play fetch or frisbee with your dog, only do so when far away from other dogs.
Find dogs with whom you think your dog would play well with, and encourage play. Sure, you can't "make" a dog play with another dog, but you can still encourage it. I and two other women will walk our dogs out away from others, and our three dogs will generally play together. (All three are between nine and ten months old, and roughly the same size.)
Don't be afraid to speak out to protect your dog's right to play in the park if it is important to you. I have been downright rude to one mother who brought in two and four year old girls who tried to "hang" on my dog. Yeah...stupid, stupid woman. I'm going to stand up for my dog's right to play in the park without me having to worry about Teddy knocking over and injuring a two year old child.
The rule is no kids under twelve years of age in our dog park, so I warned her that I would call the cops if she didn't take her kids away from my dog.
Stay vigilant and have fun, and don't be afraid to shun the clueless woman with the aggressive dog whom she ignores while texting on her cell phone. Don't go out of your way to make this person feel welcome.
Don't get me wrong: we are quite friendly and not cliqueish, but we don't "welcome trouble."