I think you can be pretty straightforward about it. Just write that you appreciate the offer and were impressed with the school, but will be attending another program. (If you are certain as to which program you will be attending, you can probably include this information too, as schools seem to keep statistics of this type of thing.) Then give them your SSN and AMCAS ID and sign the letter.
I'm reasonably sure that programs just appreciate being informed of your decision in a timely manner and don't care too much about the specific wording you use.