What are the steps for transitioning from a non-B visa to a tourist visa after quitting a job in Thailand?

If you're on the original non-B visa then yes you need to leave the country and can return.

If you're on an extension of stay then you MUST get documents from your job that say your last day of work and then go to immigration and cancel your extension before you leave. You can go about a week before the date on your documents at most immigration offices that way you don't have to to try and rush out of the country the same day.

If you are on an extension and don't do this you won't be able to get another long term extension in Thailand and you'll be fined 20,000 baht for failing to cancel your previous work extension.