There are a few things you can do to annoy your neighbor's dog. You can make loud noises, especially during the night when the dog is trying to sleep. You can also put food or other items in your yard that the dog will be tempted to eat or play with, but be aware that this could result in the dog getting sick. Finally, you can ignore the dog completely and act like it doesn't exist - this will usually make the dog very frustrated and may cause it to bark excessively.