What is the procedure to obtain a 60-day tourist visa in Thailand and transition to an education visa?

I am an American, traveling through southeast Asia since January, and I am looking to stay in Thailand longer and wanting to learn more Thai language. I am currently in Thailand on a 30 day tourist visa on arrival, that ends Oct 26, but not able to get an extension because my current landlord is not able to provide the correct documents immigration is asking for. So I will be leaving the kingdom to renew the visa, and ultimately am aiming for an education visa. I am in Chiangmai now looking at schools to find the one that will work best for me (I am differently-abled and need a slower pace of teaching style).

What I need advice on is the precise procedure needed for me to get a 60 day tourist visa. Where do I need to go, what do I need to do, how do I do it, what can I expect the process to be like and any other useful information or suggestions you might have for me, both regarding the 60 day and the educational visa.

I appreciate any help you can offer, and I apologise if I have neglected any information needed to give me the most accurate advice. Feel free to ask me anything you need to be able to help me better. Thank you!