Older non updated websites that will still show 30 day visa exempt. Some still show “only 15 days if entering via a land border”. That stopped in 2016.
If you haven’t bought a visa prior to coming to Thailand then you would get stamped in for 60 days on what’s called a visa exempt entry.
You can extend that once for 30 days at a local immigration office. There are over 80 around the country so you use the one that serves the area your TM30 (notice of staying that is filed by the hotel or house owner) is filed.
Depends on the office you use, but generally you’ll need to fill out the TM7 form (for extensions), a copy of your passport, a copy of your entry stamp, a copy of your visa, a passport sized photo a filed TM30 and 1,900 baht.
You won’t need to show an onward travel ticket and there’s an almost zero chance of being denied.