What are the etiquettes of offering the greeting of peace?

The Shaykh : ... We praise Him, seek His help, and seek His forgiveness. We seek refuge in Allah from the evils of our own selves and from the evil of our deeds. Whoever Allah guides, no one can mislead, and whoever He misleads, no one can guide. And I bear witness that there is no deity but Allah alone, with no partner, and I bear witness that Muhammad is His slave and His Messenger. As for what follows, the best of guidance is the guidance of Muhammad (peace and blessings be upon him), and the worst of matters are their innovations, and every innovation is a religious innovation, and every religious innovation is misguidance, and every misguidance is in the Fire. I wish to remind you of an Islamic etiquette, and a teaching from the teachings of the Noble Messenger (peace and blessings be upon him). It is one of the teachings that many people are ignorant of, and few of the specialists point it out. I observe that in many cases, when a person arrives, those receiving him initiate the greeting to him. This is contrary to the teaching I mentioned earlier. Also, the matter sometimes takes another form that contradicts this teaching: a man approaches a person in a car to greet him, and the person in the car initiates the greeting to him. This is also contrary to the teaching, because the Messenger (peace be upon him) said: This is an etiquette that we must observe. For example, we are arriving here; it is obligatory for us to offer the greeting, and for those receiving us to receive us with the greeting, meaning with returning the greeting. This is an organization by the Noble Messenger (peace and blessings be upon him) regarding how the greeting of peace should be offered: from the few to the many, from the young to the old, from the few to the many, and from the one walking to the one sitting.