Acceptance letters are a formal way of communicating your acceptance. This could be for an interview, a job, an invitation or any other situation which calls for your answer. It is a polite and graceful way of acknowledging something which has come your way. Writing acceptance letters to give your confirmation may be mandatory in some cases.
State your acceptance clearly in the first paragraph. Even at the cost of sounding repetitive, make sure to mention what you are accepting. You can thank the concerned party for the opportunity/invitation etc.
It is good to reiterate the terms of acceptance as per your understanding. This can help clear any issues or misinterpretations in the beginning only. This is especially applicable when you are writing a job acceptance letters. In the concluding paragraph, you must restate your acceptance and sign off formally.
These letters must be written in a polite and cordial tone as they can help to put you in a better light, both as a courteous and professional person.