With elevator doors, it is polite to allow others to enter first, but whoever goes first should reciprocate by being sure to push the “open” button to keep the doors open for the person who follows. The person nearest the button panel should ask the other passengers, “Which floor?” The others would then say, “Five please,” and always and “Thank you.”
You have undoubtedly seen in American movies how the gentleman pulls his car to stop and courteously walks around to open the door for the lady passenger. Does this actually happen? Although times have changed, a gentleman should still make the gesture of coming around to open the door. If the lady is in a long dress and high heels, she may appreciate chivalrous assistance. Nevertheless, in the modern day, the man should not be surprised when he comes around the car that she has already hopped out without assistance.
It is still customary for a doorman at a hotel or a stylish restaurant to put out his hand to help ladies get out of a car or for a crew member to put out his hand to help ladies get on or off a boat. In both cases, the woman should grasp the proffered hand, accept assistance, and say, “Thank you.” To ignore the offer or not express gratitude is rude.