What are the steps to return to Thailand after my Non-OA visa expired, and how can I obtain a new visa?

Just so you're clear, you CANNOT get a 3 month extension OR an O-A visa inside the country at the immigration office.

What you are talking about doing is comin' in on a 30 day visa exempt entry (there is no one month tourist visa :( ) then immediately applying for a 90 day Non-O visa at the immigration office by meeting the proof of funds and other requirements, waiting while it goes under consideration (for how ever long the immigration office you use takes (usually between 14 and 21 days) then going back and getting that 90 day Non-O visa stamped in your passport. THEN waiting until you have 30 days or less on that 90 day Non-O stamp and finally appying for a year long extension of stay.

If you're going to do it INSIDE the country from either a 60 day tourist visa entry OR a 30 day visa exempt entry you are going to make a minimum of 3 visits to the immigration office

one to apply for the 90 day Non-O visa

another one to go back and get the Non-O visa and your 90 day stamp inked into your passport

AND a final one when you go and apply for your yearly extension of stay.

That's why I agreed with Monti and said just get a new year-long, multi-entry Non-Immigrant Type O-A visa from a thai consulate in your country BEFORE you wing your way here

I agree with

@Mo***

, (y)

your easiest course of action would be to get a new yearlong multi-entry Non-immigrant Type O-A visa from a thai consulate in your country BEFORE you wing your way back here

Get a new O-A in Australia before returning to Thailand.