When you turn 65 you call and enroll in Part A and B. A is hospitalization coverage and B is doctor visits and tests, etc. If you have worked 10 years you are automatically eligible for Parts A and B. Part A does not cost anything. Part B in 2013 costs about $100 a month. The $100 is taken from your SS check if you are receiving one and if not you pay quarterly in advance to the government.
Both A & B have deductibles and are 80% coverage. If you want insurance to cover the remaining 20% exposure (and the deductibles) you can buy a Supplemental or Medigap policy from a private insurance company. There are 100s of different medigap policies with different deductible amounts, costs, etc.
Part D is coverage for prescriptions. There is no drug coverage in Medicare so you buy this from private insurance companies. There are dozens of different companies and types of coverage.
I have just described "regular" medicare. So for me the $100 is automatically taken from my SS check and I send a check to one insurance company for the 20% Medicare Medigap coverage (Parts A & B) and send another check to a different insurance company for Part D coverage.
The other option is Part C or Medicare Advantage - often referred to as "not regular Medicare". It is all in one shopping for Parts A, B and D and can also include dental and eye coverage. The plans are sold by private insurance companies.
With regular Medicare you pick your own doctors. With Medicare Advantage you are enrolling in an HMO or PPO.
Starting a year before you turn 65 you will begin to receive stacks and stacks of mail every day with insurance company offers.