What do I need to extend my 60-day visa on arrival in Thailand for an additional 30 days?

Visa on arrival can't be extended. You must be referring to the visa exemption scheme. Totally different things with totally different official names.

If you require any visa or extension of stay, it's always best practice to visit the immigration office you will be using, and ask for a list of requirements, because with immigration offices it can vary slightly from office to office, most will require a printed receipt of the TM30, or I've heard of some people just taking a photo of the screen after it's been completed, and printing it themselves, a while ago some immigration offices didn't require it, if there was a recent one already filed in the system, another option would be to pay to stay in a hotel for one night and get a TM30 from them (check with the immigration office some won't accept one night) depending on the office you use sometimes it's just not worth the hassle, you can just hand your passport to a visa agent and they will complete the whole process for around ฿4000.

Just go to an agent is so much easier and stress free. I paid 4600 bht have them my passport they took photos drove me to immigration strain sat in chair photo taken then photo taken outside immigration then drove me back to office picked passport up two days later.

Your landlord needs to file a TM30 (usuallu online) and you'll likely need a printed copy to get your extension or face a 1600B fine

Doubt you got visa on arrival. It's only for 15days, for certain passport holders.