It's important not to panic but get in touch with your vet immediately. It can help if you know roughly how many your dog has eaten, as well as any symptoms that they could be showing.
According to the severity and the amount ingested, the vet may choose to drop the dog and surgery may also be needed.
The advice is to keep a good eye on your dog during walks when conkers have fallen, especially if they tend to pick things up whilst out.
For more information on poisons in dogs, including symptoms and actions to take, please see vethelpdirect's poison guide.