What are the steps to apply for a retirement visa in Koh Samui, and can I get it on the same day?

First of all, you need a Thai bank account in order to be able to apply for the 90-days Non-Imm-O Retirement Visa inside Thailand

You must apply for the "change of visa type" from the 60-days tourist visa or the visa-exempt entry, to the "90-days Non-Imm-O Retirement Visa", as soon as possible after having opened the Thai bank account.

You need a bank letter confirming that the 800,000 THB are sitting in the account and a proof that they came from overseas.

You need a rental contract and you will need a minimum of 15 days stay permit left on your entry stamp in order to apply.

This application costs a 2000 THB fee, the 90-days visa will be issued for 14 days "under consideration". After 14 days you visit Immigration again and pick up the stamp

And as soon as the money has seasoned in your bank account for two months, you can apply for the "1-year extended stay permit based on retirement"

(which some people call "retirement visa" but which is NOT a "visa" but a stay permit).

This application costs another 1900 THB fee

Keep in mind, in order to get any service from Immigration, you need to be properly registered in your accommodation by the TM30 registration system

the official requirements for the "change of visa type" on Immigration inside Thailand, for your case are listed under number 9 . . . . . (change from touristic entry to a 90-days Non-Imm-O visa in case of retirement)

When you apply for a Non-O visa based on being over 50 at a Thai immigration office you need at least 15 days left on your current stamp (21 days at some offices). There's also a couple of offices that require you have the 800k baht in your bank account for 2 months before you can apply, some require it has been transferred from overseas. Your application usually gets sent to head office hence the 15 days and you usually have to return the day your current stamp runs out to get the 90 day Non-O visa stamped in your passport. I don't know the specifics of the office you plan to use so best to visit them and ask them