I was the Director of Patient Financial Services at a 325 bed hospital for 35 years, and retired 5 years ago.
So far you have been given some very good information, except that there is now Prescription Drug benefits available, but you have to buy a policy for about $20 - $40 per month.
Medicare is not an insurance, it is a federal law, so they make up their own regulations. There are in excess of 10 thousand pages of regulations for Medicare when I retired.
To be eligible for Medicare you must have worked under Social Security and paid in 40 quarters.
Medicare Part A is provided at no cost and is the part that pays for Hospital care. There is a deductible, currently $1068 for the first 60 days of hospitalization, then a "Co-Pay" of $267 each day for the 61-90 day and then a "co-pay" of $534 per day for each (Life time reserve day, which can only be used one time in your lifetime) from the 91 - 150 day. This is per "Spell of Illness", which will be broken and a new "Spell of Illness" will start once you are out of a hospital for at least 60 days.
There is a lot mere to it, but that's the basic's.
Medicare Part B. This is the part that pays for the physicians bills and all hospital out-patient services, physical therapy, lab work x-ray, etc. You have to purchase this and the premium can be deducted directly from your SS check and is $96.40 per month in 2010. Part B pays 80% of the "Covered Service" (after an annual $135 deductible), but pays the Medicare "Approved Amount", and you will have to pay the 20% of the "approved amount". ("If your physician or provider accepts Medicare assignment", otherwise you will have to pay it all.) Make sure your physician will accept assignment. Most do, but with the "new" government interference many may change their minds.
Medicare Part D. This is the part that pays for prescription drugs. You have to buy a Medicare approved insurance plan, and there are many which all pay different amounts on different drugs. This is where you really have to shop for the plan that fits what drugs you personally need to use. It is not unusual for a husband and wife to each have different policies as they have different drug needs. There will be "Tiers" with different co-pays for drugs in different tiers.
Unless you are wealthy, you need a supplemental insurance policy, and there are a lot of them, and you need to shop as there can be over $1000 per year difference between plans.
My recommendation is to locate an Insurance agent that specializes in Medicare supplements and Long Term Care policies. Ask around you will find friends and associates that will be able to recommend one. Start at least there months before your 65 to get it all lined out. There should be a Senior center in your area, and they can also help direct you.
Good luck, This was just a tip of the iceberg on the whole subject. Medicare produces a booklet, "Medicare and You" each year with all the new changes. There should be one available at your local Social Security office. Get one and read it for more information.