You can enroll in Medicare, if you are within 3 months of the month you turn 65. For example, if your birthday is July 5th, then you can enroll online as soon as April 1st and no later than October 31st.
On average, Medicare Enrollment takes 2-4 weeks to process. If you are already on Social Security your enrollment is automatic, you do not need to apply.
Note: Different dates may apply, if you have been on Social Security Disability for at least 24 months.