I've noticed this month how proud many expatriates are to say "Assalamu alaykum" or "Ramadan kareem" and soon "Eid mubarak". And so they should be; thank you for making this effort. But whereas westerners usually respond to greetings such as "Merry Christmas" with "Merry Christmas to you, too," Muslims are different. It is suggested in the holy Quran that we should do our best to extend any greeting we receive.
There is a nice story that illustrates this. A man named Abdullah lived in a small village and walked a good distance to the bazaar each day. He would walk around to each shopkeeper and greet them with "Assalamu alaykum", then walk back home. One day, as he was about to head back to his village, the last shopkeeper approached him. "Abdullah, you walk all this way, yet you never buy anything. Why?"
"I come to the bazaar to offer salaam to the people," replied Abdullah. "Not for shopping." The point is that Prophet Mohammed wanted to spread compassion among his people. If you are looking at demonstrating your knowledge of Emirati social codes, start with extending your greetings. Instead of saying "Eid Mubarak", for example, add: "Allah yebarak feik", which means "and may God bless you".