Address the letter to your advisor. If you don't know who your advisor is, call your academic department and ask for her name. Begin the first paragraph by explaining right away that you would like to change your major. Give the full name of the degree program you were in and give the new program. If you will switch your minor as well, provide that information too. For example, write "I would like to change my degree plan from a B.S. in Chemistry with a minor in Biology to a B.S. in Biology with a minor in Psychology."
Explain the reason that you are changing your major in one paragraph. For instance, "I am interested in changing from a chemistry major to a biology major because I have decided that I would like to pursue a degree in medicine after my undergraduate degree, and a degree in biology is more applicable to medicine. I feel that a minor in psychology will help me understand the trauma that patients with severe injuries go through, which will help me become a better physician."
If your new major is in the same academic department, such as moving from a B.A. in Literature to a B.A. in Technical Writing within the English Department, you will probably retain the same advisor. Ask your advisor (in the letter) for an appointment to sign any necessary forms and to discuss the specifics of your new degree plan. Changing your major might change your graduation requirements. If your change in major places you in a different academic department, contact the new department for advising.