1st post already covered everything you need to know about CM, but I'd like to note something that I had a massive amount of trouble with the first time I went into CT (never caused a wipe but gave me a huge headache): During the fight where you're waiting on Cid to do "a thing", your co-tank will be tanking a Giant. During this time, Garlean adds will pop up and start murdering your healers. It's your job to go grab those, and at first it's pretty easy. But the 2nd to last wave and final wave can get a bit hectic.

I'd recommend telling both healers to stack in a certain place (I put them on the other side of the ramp that the MT isn't on) so that all adds go to one place and you don't have to run around like a chicken with your head cut off. Just make sure to get the adds off (Overpower/Steel Cyclone/Flash your butt off) your healers before they get killed and you're golden.

Thankfully, until off tanking T4 in phase 6, you'll never have to deal with this massive annoyance again. So glhf!