I've heard that after 5 years residency, you can buy in to Medicare part A and part B even if you don't have the necessary 40 quarters of contributions. Its likely to be expensive, but there are few other insurance options.
Prior to the 5yr mark, you have to take private insurance, if you can find a carrier that will cover you. The big problem is that most carriers are not interested in people over 65yrs of age. Any coverage that is available is likely to be very expensive. There are a couple of providers with special immigrant policies, and if you do some more research here, you will find references to their websites.