If you join before December 7, 2019, your drug coverage will begin on January 1, 2020. The Centers for Medicare and Medicaid Services suggests that you enroll in a plan as soon as possible to minimize any potential problems with your coverage beginning on January 1.
If you are currently enrolled in a plan, but have enrolled in a different one for 2020, your current plan will cover your drugs through December 31 and your new coverage will begin on January 1, 2020. If you enroll or change coverage during a Special Enrollment Period (SEP), the effective date of your coverage will depend on the reason for the SEP.
If you first become eligible for Medicare Part D at any other time — for example, if you turn 65 part way through the year — your coverage will start in the month you become eligible if you joined in the first three months of your Initial Enrollment Period. If you sign up during the last four months of your Initial Enrollment Period, you become eligible the month after the one in which you joined.