Clemency, like all healing skills, is a skill that is best used with foreknowledge of how a fight plays out.

In a general sense, a dozen or so people have already put it out right, "Use it when you think/know it will help."

From what I experience day to day, quite often healers will raise someone in general content, and then not do enough to prevent them from dying to the next raid wide. That's a good time to Clemency.

You can also use it sort of like an extra cooldown in dungeons. Like say your healer is a bit slow on the uptake, and they don't/won't use their whole kit. Your DPS are good, so you want to pull a lot, but the healer isn't, so you might die. You pull everything, and you rotate through every cooldown for one pull. Then the next, you can keep yourself up with Clemency, usually long enough for other CDs to come back. Just watch your HP and the activity level of the healer. If you know your HP is depleting faster than they're keeping up, and you've kept track of their oGCDs used on you in the last pull vs. the dungeon timer, than it's safe to Clemency, guilt free.