"The customer is always right" may be a misleading cliche, but complaints are part of any business, particularly one like a restaurant that includes both products and service. Getting defensive over complaints is easy because they feel like criticism, sometimes seemingly unwarranted. However, by handling a complaint the correct way you can often placate the customer and improve your business.
Take a quick look through the complaint letter and see if the facts of the case are simple once you've got past the customer's emotions. Decide whether the case will need further investigation.
Respond to the customer quickly if the case is clear-cut. Acknowledge the customer's disappointment, apologise for any mistakes or inadequate behaviour on behalf of the restaurant's staff, and explain what actions you will take to make sure it does not happen (or is less likely to happen again).
Offer some form of compensation such as a free meal if you think it is justified. This can greatly reduce the chances of losing a potential regular customer, or having the customer bad-mouth you to friends. However, don't be afraid to not offer such compensation if you believe the complaint is malicious or ill-founded.
Respond to the customer quickly even if the case is more complicated: acknowledge the complaint and say you will investigate further. A quick acknowledgement will make it less likely the customer will act angrily and tell friends or post about the incident on social media.
Investigate the case in detail if necessary. Ask the customer if you need any more detail such as the time and date he visited the restaurant. Talk to the staff who were working at the time, but make it clear you are investigating rather than accusing.
Write to the customer when you have concluded your investigation. As with an immediate response, acknowledge the problem and detail your response. Do not get overly defensive or try to make excuses (even if you see them as reasons). Be polite and professional.
Avoid getting into a drawn-out exchange with the customer if she is not happy with your response. Just make sure you have responded in a reasonable manner.
If the complaint is something that might turn into a legal complaint, such as the suggestion you have caused food poisoning, be more cautious in your response. You may want to avoid admitting responsibility until you know the full facts of the case. Take care with your wording: for example you can say you are sorry the customer became ill, rather than that you are sorry your food made the customer ill.