To write a letter requesting a meeting, keep your letter short and to the point, with your request made at the very beginning of the letter. Make it very clear that you are requesting a meeting and why you are making the request. Provide reasons or incentive for the person to whom you are writing to grant your request.
A letter requesting a meeting should be very short, no more than two paragraphs. In the first paragraph, introduce yourself if you don't already have a relationship with the person you are writing to, perhaps stating any mutual relationship or connection you have. Make the request immediately afterward. Be specific about your reasons for the meeting. State clearly if you are seeking a job interview, want to make a sales pitch or are seeking more information regarding a specific topic. Let the person know the length of time you hope to talk to them.
In your second paragraph, add any relevant information that is likely to persuade the person you are writing to that it is in their best interest to grant your request. Also use this second paragraph to outline any further contact you expect to have, indicating, for instance, whether you are going to call during the next week to follow up on your request.
Make sure your letter is written well and contains no spelling or grammar mistakes to ensure that your request for a meeting is received as well as is possible.