Some of the things others have mentioned are great tips. I will go a bit further and say it really depends on who you are playing with. Most of the guys I play with are good players but are not real strict on everyone staying on the green until everyone is done, waiting until someone leaves the tee box to approach for their tee shot, etc. We play on a busy course and know to just play ready golf.
That all said, playing with folks you do not know or never played with, try your best to follow etiquette unless they tell you otherwise. I have played with new folks who told me after a few holes not to be worried about perfect etiquette and then some who made it well known by their actions they are strict about it. Just know your playing partners.
The absolute do's to me are:
1. Never walk on someone's putting line
2. Repair Divots (it amazes me how many do not)
3. Do not talk during someone's swing
4. Turn the damn cell phone ringer off and if you have to take a call, leave the area where others cannot hear you.
5. Do not drop the flag down on the green. This is one many folks do and do not realize the damage it can do to a green. Gently lay it down.
6. Help others look for their ball and unless in a tournament, look for 2-3 minutes and play on.
7. I like to help my partners by handing their clubs, towel, etc. when on the green to speed up play and also help make up for anything I have done that might have annoyed them. Its just a nice gesture that helps.
Main thing to remember is that noone is perfect. We all are going to or already do something that annoys someone else. Just do your best and always keep pace of play in mind. If your group is too slow, be the person who steps up and asks everyone to speed up some. I am usually that guy because I hate waiting and always just tell my partners (unless the groups in front of us are backed up as well) to start playing ready golf. Never had anyone not agree and we play faster and make the day enjoyable for everyone. I always feel that everyone on the course should respect one another no matter what hole they are on. I think treating the course well is good karma and I can always use some during a round.