Be persuasive.
Establish a positive relationship with your reader right away. If you have a connection to the reader - you've met before or have a mutual colleague, for example - mention it in your introductory paragraph. Whether you think your reader will agree with the point of your letter or not, it is important to find common ground and build your case from there.
Understand your reader well enough to anticipate how he or she will react when reading your letter. Address his or her needs or wishes, or a specific problem, and then outline your solution. Provide proof in the way of examples and/or expert opinions to back up your point. Make sure to maintain a friendly tone.
Conclude your letter with a "call to action." State clearly what your reader needs to do or believe to achieve the desired solution and then state what you, the writer, intend to do next to follow up.