Dogs are allowed on some beaches as long as you keep the dog on a leash and they may have certain areas marked off that prohibit dogs on the certain areas of the beach.
I've seen some beaches that didn't allow dogs and then some beaches did and do allow dogs as long as the dog is not a mean dog and is good around people.
You must keep control of the dog at all times and if it bites someone then you're responsible.
I would personally keep a dog at home and go to the beach without the dog but some dogs I've seen on the beach were having fun with the owner and the owner of the dog was having fun as well.
If the beach doesn't allow dogs then there will be signs posted but most of the beaches I've been too allow dogs to play on the beach.
You must also pick up their poop if they do poop on the beach and that's the right thing to do as well.