You may begin your enrollment in original medicare up to 3 months prior to your effective date. Your effective date is the first of the month in which you turn 65. (if you were born on the first of the month you effective date is the first of the preceding month.)
The Medicare website - www.medicare.gov is an excellent resource to learn about Medicare and what it offers.
Another great resource is the following video from Unitedhealthcare that explains Medicare in an easy to understand format.