Enrollment

The best time to buy a Medigap policy is during the 6-month period that begins on the first day of the month in which you’re 65 or older and enrolled in Part B. For example, if you turn 65 and are enrolled in Part B in June, the best time for you to buy a Medigap policy is from June to November.
After this enrollment period, your option to buy a Medigap policy may be limited and it may cost more. Some states have additional open enrollment periods.

Medigap insurance companies are generally allowed to use medical underwriting to decide whether to accept your application and how much to charge you for the Medigap policy. However, if you apply during your Medigap open enrollment period, you can buy any Medigap policy the company sells, even if you have health problems, for the same price as people with good health.
If you have group health coverage through an employer or union because either you or your spouse is currently working, you may want to wait to enroll in Part B. Employer plans often provide coverage similar to Medigap, so you don’t need a Medigap policy.
When your employer coverage ends, you’ll get a chance to enroll in Part B without a late enrollment penalty which means your Medigap open enrollment period will start when you’re ready to take advantage of it. If you enrolled in Part B while you still had the employer coverage, your Medigap open enrollment period would start, and unless you bought a Medigap policy before you needed it, you would miss your open enrollment period entirely.
Cost

Medicare doesn’t pay any of the costs for you to get a Medigap policy. You have to pay the premiums for a Medigap policy.
Medigap helps pay your Part B bills
In most Medigap policies, when you sign the Medigap insurance contract you agree to have the Medigap insurance company get your Part B claim information directly from Medicare, and then they pay the doctor directly. Some Medigap insurance companies also provide this service for Part A claims.
If your Medigap insurance company doesn’t provide this service, ask your doctors if they “participate” in Medicare. This means that they “accept assignment” for all Medicare patients. If your doctor participates, the Medigap insurance company is required to pay the doctor directly if you request.
Compare the costs of Medigap plans
Insurance companies may charge different premiums for the same exact policy. As you shop for a policy, be sure you’re comparing the same policy (for example, compare Plan A from one company with Plan A from another company).
In some states, you may be able to buy another type of Medigap policy called Medicare SELECT. If you buy a Medigap SELECT policy, you have rights to change your mind within 12 months and switch to a standard Medigap policy.

Complete Medicare information at the official U.S. government Medicare site