Do not compost pet waste as it will kill your plants. The best way to dispose of dog waste is to pick it up in a bag and put it in the garbage. There are companies that will come to your house and dispose of the waste for you for a fee.
Call the owner of the dog and tell them to come clean up after their dog. Or you can scoop it up and put it in a bag and put it out with your garbage the garbage company will take it no problem. Or you can start a compost pile and use it there.