What should an Australian do if he has overstayed his tourist visa in Thailand by one month?

Actually it doesn't matter if he's on a 60 day tourist visa OR a 30 day visa exempt entry. IF he has a month overstay he can't get any extension on it because they only issue a 30 day extension dated from the date your entry stamp expires.

He could go to the immigration office pay the overstay fine of 500 baht a day and then immediately get an "extension of stay denied" 7 day stamp to get out of the country. That would at least make him legal for a week so he can leave the country rather than chance the fact he'll get caught out on something else while on overstay <-which will open a whole different can of worms for them..

So he's on a 60 day tourist visa that he got from a thai consulate in another country?

If he goes to immigration or is stopped by the police, its likely he will be arrested and deported

Hes got about a 10% chance of them extending his visa. Genereally would have to be under good circumstances. He can jst turn himself in when he flys out pay the fine of 500 baht per day / max 20k baht ..

on the way out leaving the country - at the airport - leave now