You have probably applied to many schools and the application process may have been quite nerve-wracking. Nonetheless, be sure that you are addressing your acceptance to the proper person and school. The last thing you want is to come across as disorganized and unfocused when accepting a graduate school admission offer.
Although you are probably excited when you find out that you have been accepted into a graduate program, maintain a courteous and gracious voice in your acceptance of a graduate school admission. This kind of voice will involve the mention of your excitement at the prospect of being able to study with certain professors, your fellow students, and within the department at which you have been accepted.
It is always wise to confirm a graduate school's estimation of you, even if you have already been offered admission. To help cement your dedication to graduate studies in the mind of the professors and faculty members that will review your acceptance letter be sure to mention that you have chosen that school after serious consideration of other offers.
Be clear and direct about why you have chosen the graduate school that you have. This explanation will show your future professors that you have clear reasons for attending this particular graduate school. Mentioning these reasons, even if you do not think that they will remain throughout the course of your graduate studies, will also show your motivation and dedication to graduate work at this particular school.
If you met or corresponded with any professors while you were working through your decision about accepting a graduate school's offer, then be sure to mention them in your letter of acceptance. One effective way to work this mention into your acceptance letter is in the form of a narrative. For example you could write: "After my correspondence with Professor X, I was entirely certain that the University of Y was for me...)." The professors and faculty members who arrange preacceptance meetings with students put a lot of effort into them, and even a small mention of such a meeting in your letter can show your appreciation of this effort.
As a separate consideration, it is also important that you notify all schools to which you were accepted but will not be attending about your decision. Letting the other graduate schools know about your decision to not accept their offers of admission will allow them to take you off of their list of candidates for admission. This will then allow these schools to extend an offer of admission to a wait-listed candidate. Be as sure to be as gracious in notifying schools that you will not be attending them as you are in notifying the school that you will be attending about your decision to do so.