1. Display a willingness to listen to the complainant.
2. Find out not only what the complainant's problem is but also what he/she would like doing about it. (e.g. if someone complains about the non-delivery of a product which you're company is waiting for new supplies of, find out whether they want a refund, a replacement or simply to wait a little longer).
3. Assure the complainant that you'll investigate the matter thoroughly and get back to them as soon as possible but don't commit your employer to any course of action at that time unless it's crystal clear that they've got a valid complaint and an immediate solution (acceptable to both the complainant and your employer) is obviously available.
4. Otherwise don't assume either that the complainant has a valid case or that they're simply 'trying it on'. Make sure that you're in full possession of all the facts before making a judgement.
5. If the complaint is found to have no real basis, and thus requires no action from your employer, get back to the complainant as quickly as possible and politely explain why you're unable to help them further. (If there's a body which the complainant can then turn to if they're still unhappy, such as an industry ombudsman, ensure that the complainant is provided with the relevant information about appealing to that body).
5. If the complaint is found to be genuine, assess the means of redress available to you. If what the complainant asked for (e.g. a replacement product) is among those options then use that form of redress. If, for some reason, it's not, contact the complainant to explain your problem and to seek an alternative mutually satisfactory solution.
6. Consider whether, as well as providing a replacement item (or whatever else is appropriate to the circumstances), it might be in your employer's best interests to make a further gesture of apology (such as sending the complainant a cheque) in order to ensure the best possible public relations for your employer's company.
7. Always work as quickly as possible when responding to complaints. If some form of delay will be inevitable (such as awaiting the arrival of new stock), ensure that the complainant is kept informed of what's happening,so that they can see that they're not simply being ignored.