Everyone has to say the words, "I'm sorry" at least once in a relationship with another person. Business relationships are no different. The way in which the apology is delivered can often make or break a fragile business relationship. Thus, proper care should be given so that you can write a business letter of apology without causing even more harm.
Understand the situation. Before you sit down to write, you must know what it is that caused the situation for which you are apologizing, how it is being fixed and how it will be avoided in the future. You must also know what legal ramifications are involved so that you can skirt those issues in your business letter of apology.
Apologize in the beginning. The very first words in a business letter of apology should be some formal saying of the words, "I'm sorry". This lets the recipient of the letter know exactly what your stance is up front. It also softens him for the explanation to follow. This part should be one sentence long and tell clearly, but concisely what the apology is for.
Explain yourself. Here's where you get to tell the other person or company just what led to the situation in question. It may have been a misunderstanding, maybe an oversight. Whatever the problem was, explain in detail. However, do not rant or try to gloss over the situation. Just state the facts in the best way possible. This section may be a sentence up to a paragraph in length.
Make up for the wrong. Tell the recipient exactly what you did or are doing to rectify the situation. Leave out the fluff, but try to be a detailed as possible. Also, add how the company plans to avoid such an issue in the future. Again, be detailed, but leave out the fluffy speech. You are not trying to sell anything here. In addition, hyperbole can come off as insincerity, so avoid it.
Sign it in ink, not a stamp. You hand signature is yet another personal touch to show sincerity. A printed or stamped signature reeks of form letter. As a result, the business letter of apology will seem like either a brush off or an insult. This will only make the problem worse.
Proofread you letter before mailing. Take the time to edit out typos to make your letter of apology reflect your professionalism.