How does one apply for Medicare?

I am looking down the road a bit and trying to figure out how a person applies for Medicare. What age do you have to be? When do you do it? What are all these "plans" I hear about on TV? If one spouse is on Medicare and one isn't what does the non-insured spouse do for insurance coverage? What is supplemental ins?
If anyone has applied recently, could you please shed some light on the subject? thanks