Short answer: Apply through Social Security, online or by calling 1-800-772-1213 to set up an appointment. The application can be filed any time, before or after the person joins a Part D plan, and it can also start a Medicare Savings Program application with the state.
Social Security takes Extra Help applications online at ssa.gov or by appointment (call 1-800-772-1213, TTY 1-800-325-0778, and ask for an appointment to apply for Part D Extra Help). There is no enrollment window: the person can apply any time, before or after enrolling in Part D.
Have these ready for the person and spouse: bank statements and tax returns, IRA or 401(k) balances, and statements for pensions, veterans benefits, annuities and Railroad Retirement benefits.
Medicare.gov notes that the Extra Help application doubles as a start on a Medicare Savings Program application: Social Security sends the information to the state unless the person opts out on the form. The local State Health Insurance Assistance Program (SHIP) gives free help applying.
People on full Medicaid, a Medicare Savings Program or SSI do not need to apply; they get Extra Help automatically.