He is already on Social Security, so Part A, which is free, is automatic. Part A pays the hospital bill. It does not pay any doctor bills. A couple of months before he turns 65, he will get a packet from Medicare. It includes a Medicare card with a membership number. If he wants to skip Part B, which pays for the majority of doctor bills, he has to sign a form and mail it back. If he does not do that, the premium for Part B will automatically be deducted from his Social Security payment, beginning with the month he turns 65.
There is a "Welcome to Medicare" pamphlet in the package. It's online, and I suggest you read it before you talk to him. In addition to Part B, there is drug coverage under Part D, which has to be purchased. It's voluntary. There are also Medicare supplement policies, called "Medigap" policies. They pay most of what Part B does not pay.
He is probably not a candidate for Medicare Advantage, which has lower premiums, because of high out of pocket expenses in some circumstances.
In addition to reading the Medicare information, you may want to have a look at some of the videos on SeniorSavingsNetwork.org. The guy that produced those videos sells the various supplement plans, but the videos are very helpful in understanding how the various parts of Medicare work. It's in your and your mother's best interest to understand Medicare to minimize the financial damage from your father being uninsured can do.