Simply replace the unfilled areas such as "" and "[date]" with your information.
Dear [Name of supervisor],
I have enjoyed working for you for the past [time period working for supervisor], and felt that I have learned a lot about our company and department. I have enjoyed building my skill set, and would like to thank you for all the encouragement and opportunity that you have given me.
I feel at this time that I am ready to take on more responsibility within our department. I understand that management positions are few, and I am not asking for that at this time. Instead, I am asking to be allowed to prove my leadership skills by helping to lead some projects within the department, or by being responsible for a day-to-day process.
Please allow me to help you with daily functions, while at the same time proving myself and increasing my skills.