Determine what went wrong -
Forest fires in his country, set by farmers to clear fields, created air pollution problems for neighboring countries Malaysia and Singapore. He wasn't beating around the bush about this one.
Take full responsibility -
The fact is the haze originates from Indonesia, there're no ifs and buts, "so we take responsibility" was the clear commitment conveyed to the press. Hence the "massive handling, deploying more officers" initiated by him personally in the past two to three days.
Choosing the right time to apologise -
The "megaphone diplomacy" - kicked off by one Singapore minister's posturing Facebook post - was getting out of hand. Of his "one statement (about dining out options) which will haunt me for my entire political life", Vivian Balakrishnan had admitted, "unfortunately for me, I'm one of those ministers who likes to speak without notes and sometimes I make mistakes" (still does). Fortunately for us, President Yudhoyono averted World War III.
Speak softly and carry a big stick -
Make no mistake, the leader of the fourth largest country on earth (behind just China, India, and the US) is no push over. He made it clear that there will be no impact on Indonesia's bargaining position, namely on the territorial disputes with Malaysia or the return of ill-gotten assets of corrupt Indonesians living it up in Singapore. On subject of a mutually respectful Asean spirit, he put on record his personal feeling that Singapore media reporting on the haze issue has been "excessive" and "put Indonesia's image in a bad light globally."
Now compare it to the other guy's apology, "we’re sorry we didn’t get it exactly right, but I hope you’ll understand and bear with us, because we’re trying our best to fix the problems." And they are still trying to get it right - housing affordability, hospital shortages, train disruptions, over congestion, cost of living, etc - and the only light in the tunnel is still hazed over.