What do I need to do to extend my stay in Thailand until January 24th as a New Zealand passport holder?

Umm, you don't need to check when you get back to your room. Answer the question on whether you BOUGHT a visa from a thai consulate in your country BEFORE you washed up here OR whether you showed up without a thai visa in your passport and were stamped in for 30 days for free.

IF you are on either a 60 day tourist visa entry OR a 30 day visa exempt entry you can extend that by 30 more days ONCE at the immigration office that serves the area where you stay for 1900baht.

On what basis did you enter ? 30 day exemption ? If so, go to immigration and apply for a 30 day extension for the princely sum of 1900 THB.