I attended a letter of recommendation workshop, and they gave me a template similar to the following for requesting a letter. They also recommended even writing a draft of a letter for the person you are requesting it from, so they get an idea of what to write if they aren't used to writing letters.
Your First and Last Name
Street
City, State Zip Code
Month Date, Year
Letter Writer's Name
Position, Where
Address of Work Location
City, State Zip Code
Email Address
Dear [Letter Writer's Name],
Please consider my attached application for a letter of recommendation. Enclosed you will find all the documents required for me to complete my application. I am applying to X programs in X month. I am requesting to have the letter of recommendation completed by [Month Day, Year] so that I can submit my applications as soon as possible. Optional: I have included X envelopes because I will be mailing one letter to X, which is the online application service for a few schools I am applying to. The other X letters will be mailed to specific schools that do not use X. I would appreciate if you could also sign the back of each envelope once sealed.
I know that letters of recommendation are heavily weighted for X programs, and I am confident that you will provide me with a strong recommendation. I have waived my right to view your letter, so please be honest and sincere in what you write. Some suggestions of what to include are provided below. Feel free to organize the letter as you like and include any other relevant information.
Who you are/how you know me
My potential/promise as a medical professional
My intellectual curiosity / creativity/ capacity
Particular contributions I have made
Ability to thoroughly complete assigned tasks on time; ability to work independently
Interpersonal skills
Leadership ability
Communication skills
Personal characteristics: reliability, maturity, independence, commitment, dedication to helping others, etc.
Thank you so much for taking time out of your busy schedule to write my letter and help me reach my career goals. I have gained a lot from your teaching, and appreciate the opportunity and experiences that you have provided as a mentor. If you have any questions regarding my information or anything, please feel free to contact me.
Sincerely,
Your Name
[Academic Email]
[Non-Academic Email]
[Cell Phone]