Even when you do get a group together via the Group Finder (and not the "old-fashioned" way), communication is always going to help your group be successful. Now that the Group Finder is out, lots of players may be trying out Flashpoints or Operations that they haven't tried before.
If you've never done the content before, it helps to speak up! Let your group know with something as simple as, "Hey, I've never beaten this Flashpoint before - can someone explain the bosses/mechanics to me?" Generally, someone else in the group will be able to offer you a brief explanation. Letting people know that you've never been but are willing to pay attention and learn is always much better than making a mistake!
If you have done the content before, you can help by stepping up to explain. Some people may be afraid of how a group will react if they're new, so take the lead and help! If someone seems to be having trouble (or if they're doing something wrong) and you can offer tips, do it! Remember, everyone has to do something for the first time once, and it doesn't help to get upset with people right away - give people a chance and some explanation and encouragement.
Good communication is definitely a key to success, so speak up!
Agreement: This kind of thing needs to be heard.
Addendum: I would like to add that SAYING WHO'S DOING WHAT (eg. who's CCing what enemy) helps too. Not just going in and expecting people to predict your actions.