A letter requesting something should be written with an introduction, the request, any details that the reader may need and a call to action with specific deadlines. The length of the written request is typically shorter if the request touches on a reward for the reader and longer if it does not because the latter requires additional persuasive writing.
The introduction of both the writer and the request should not take more than two sentences. Give the additional information to the reader in the opening paragraph for simpler requests or in the second paragraph for longer requests. The addition of persuasive writing may necessitate the inclusion of a separate paragraph dedicated to explaining the reasons it is in the reader's interest to fulfill the request. If the request is for three or more things, use bullet points to help make the request more clear.
The final paragraph should include a call to action, which is what the writer is specifically asking the reader to do. Restate the initial request in this section, and add any pertinent deadlines by which a response is required along with an explanation of why these dates are important. If the request involves making a payment, ensure that the final paragraph has all the relevant payment details that the reader needs.