Format your letter so that it will have one-inch margins; this is the standard for business letters. Then adjust the type so that your lines will be single-spaced and aligned left. Finally, set the typeface to Times New Roman, Garamond, or another typeface with serifs or "feet" at the top and bottom of the letter; these typefaces were designed for the printed page and they appear more professional.
Type your address, without your name, at the top of the page. Skip a space and type the date. Skip another space and type in the name of the graduate coordinator (typically the person who notified you of the acceptance), her title, department name, university name and department address.
Address the letter to Dear Dr. (name of graduate coordinator). A graduate coordinator almost always has a PhD; address her as "Dr." in any correspondence.
Begin the letter by stating that you accept your position as a graduate student in the school. Be very specific and name the department and degree program, as the graduate coordinator will probably forward the letter to the graduate school, which is a separate department at the university.
Mention any other positions or associated awards and accept those as well. You will receive additional contracts to sign for your graduate assistantships and fellowships, if applicable, but they will appreciate knowing your intentions.
Express appreciation for the position and remind them of your contact information in the closing paragraph.
Close the letter by typing "Respectfully," then skip three lines and type your full name. Print the letter and sign your name in blue or black ink above your typed name. Retain a copy of the letter for your records.