Open enrollment for Medicare Part B medical insurance starts January 1 and lasts through March. If you did not sign up when you were first eligible, you can do so now. Medicare medical insurance helps to pay for doctors' services, home health care and a number of other services that aren't covered by Medicare hospital insurance. If you sign up between January 1 and March 31, your coverage begins in July. But remember: you must sign up before the end of March.