Most people will automatically receive their Medicare card a few months before they turn 65. You will be automatically signed up for Part A and Part B in most situations.
You can decline or postpone Part B if you wish. The only reason I can think of for postponing Part B is you have existing coverage through an employer group health plan and that plan is primary.
On a side note to Mr. Vineyard's answer which is great , once you receive the Medicare claim number which is usually your social security number with a letter behind it, this will allow you to sign up for a Medicare Advantage Plan. These plans are offered through private insurance company's like Aetna, United HealthCare, and Humana and have to be at a minimum as good as original Medicare but these advantage plans almost always have added benefits such as dental, vision, and hearing that original Medicare does not have. Most company's have several plans available at a $0.00 monthly premium in addition to your Part B premium. Original Medicare only covers 80% and you pay 20%. There are no co-pays.
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You can decline or postpone Part B if you wish. The only reason I can think of for postponing Part B is you have existing coverage through an employer group health plan and that plan is primary.