Although Walnuts can be toxic to dogs and cause health problems such as hyperthermiain, Lethargy, Tremors and even weakness of the hind end your dog will likely be okay after eating one Walnut.
If your dog ate just one Walnut then I would just keep an eye of them for any out of the ordinary things that the dog may be experiencing and take them to the vet if you're concerned about the dogs health.
Although if the dog ate just one Walnut the dog will usually be fine and not require any medical treatment.
If the dog ate more than one Walnut then I would advise taking the dog to the vet.