I half expected to see the first post be "Best WHM Advice: Reroll AST"
Glad people have more class than that.
Onto the advice: I don't know if I have anything to add that those before me haven't already posted. But I can relay some personal tweaks and optimizations I use when in fights.
If you got Largesse on your bar, Largesse + Regen on a tank will usually mitigate any damage they're taking sufficiently enough for you to have 15-20 seconds of attacking going on before the tank needs to be touched again. At higher levels, if Largesse is down, Regen + Asylum will also work so you can continue hammering the mobs. Again for higher levels, once you're down to just Regen, and the tank is like 60% toss Divine Benediction (DB) with Regen and see if that will heal the tank up a bit so you can keep attacking. If not, pop Tetra on him and keep pounding. By that point, Largesse should be back up and the process continues.
When it comes to using Holy, everyones favorite eye blinding spell of spam, after the tank finishes pulling I throw on a Largesse Regen then immediately swiftcast the Holy. The tank is gonna take a huge damage spike by the time that first Holy gets off because all the mobs finally catch up to him, but Holy stuns, so he's perfectly safe for like, 4 seconds. This buys a lot of time for the DPS to hammer the mobs and help mitigate the damage to the tank. There's also plenty of time to oGCD a Tetra or a DB and start Hardcasting a second Holy as Regen takes care of him. Then you ramp up into the spam. Just keep casting it until you're out of oGCDs to save the tank in between casts or all the mobs are dead.
It's a bit risk reward. Part of WHM and healing in general is gauging how fast your tank's HP sinks during a typical 4-5 mob pull and if your Healing over Time (HoT) spells are enough for that. If the tank is really poorly geared, or over ambitious, you'll have to cut back on relying on your HoTs and start babysitting their HP bar with oGCD heals.