Excellent post, NeoAmon.
A note to those who never did Coil but have prior raiding experience in other MMORPG's: say it!
I'm such a player and I can tell you that if you've cleared raids in other games, such as WoW (at least normal difficulty level, not talking about LFR, as for flexible I just don't know) or Rift, chances are you're definitely skilled enough for Coil which (at the notable exception of Turn 5), isn't that hard. So just state your prior experience, it'll give raid recruiters the reassurance they need, knowing you're the kind of player they're looking for.
Also, doing a bit of research isn't a bad idea. When you're commuting from/to work, during your breaks, while waiting for people to answer your shouts, or waiting on your AK/WP DF to pop…

Just don't lie your way in saying that you have experience just because you've watched a video, but it certainly helps to have an idea of what you should be expecting (a video helps you know the
visual cues and the
mechanics, the
general proceedings of the fight; and if you really want to know the theory, a written guide will provide very detailed and specific knowledge such as "attack X of boss Y does Z damage to n players every T seconds" and so on). I'd be more favorable to take a pick-up player who says he/she did a bit of research, even just a 2 minutes video, than someone who has no clue and flat out doesn't care. (unfortunately for FFXIV there aren't many videos since SE is taking them down when they're edited with voice, based on their archaic ToS which is totally out of touch with YouTube gaming videos, but that's another topic entirely; you can still find some strategy videos for this game).
On a side-related note, I'm not saying one
must do prior research to raid in games; this is just advice to maximise your chance to get a group. I
personally prefer to go there and figure out a strategy as we progress, depending on the group (classes etc.), but I usually raid in a static (or like-minded individuals) that I usually organise myself, so I don't need to convince anyone about anything. Should you need to though, it's always a good idea to put as many chances as possible on your side!
And again: don't lie! I'll always prefer an honest newbie who's willing to learn and put effort into something (who's a real team player) than a dishonest lier who won't ever own his/her mistakes and is just not that respectable a person—how could I trust someone who lies to me?