I spent too many years in a raiding guild in another game, so I now I enjoy being guild-less and just doing my thing on my own time.
As such, I make liberal use of the Group Finder and this is how it goes when I enter a FP:
1) Say "hello" and use my class buff.
2) Check group composition. If anyone is looking ubercool in matching gear I compliment them on their look
3) If there is another player of my class (or more than one) I quickly inspect them. If their gear is better than mine, I'm needing on stuff I need for my class. If their gear is worse I'm greeding/passing on stuff.
4) When we get to a boss: if I don't know the fight I say so and ask what I should do; if I know the fight I ask if anyone is new to the fight and give a quick explanation if needed.
5) If something drops that one of my companions can use, I wait until all have rolled and IF NOONE NEEDED I ask if I can need for my companion. If the answer is "yes" I need. If the answer is "no" I greed and take my chances like everyone else.
Never had any loot stress in a PUG.