Something people will tell you not to do, and I used to as well, is not to use regen before a pull. (dungeons, not bosses)
Honestly with how bad my tanks are 99% of the time, I suggest starting with regen. Just make sure to stay within the tanks location, so the mobs on you dont leave the range of their AoE.

Before I would have to use an instant cast heal or 4 to keep the tank up as they drag mobs to the 2nd+ group of mobs, and then once I plant myself down to start healing, I get targeted by an AoE that will kill me, and if I move, I have no instant heals to save the tank, whos at a constant 25% hp or lower mid cast bar.

Your CDs will semi help keep a tank from dieing, but eventually you'll be out of CDs, and the tank will go down faster than you can spam cure2.
just hope they might actually pop a CD, or actually get gear on their tank 1st, before large pulls. (looking at tanks in i255 gear in bardums run)

even if they are in the gear from the prior dungeon, they WILL take a MASSIVE beating from 2 group pulls, and lightly using CDs.
save 1 emergency oGCD heal for when ur forced to dodge, and use the rest to fill in when they die faster than cure2 spam is healing them.

also ALWAYS look at their gear at the start, and their CD usage at the 1st pull.
if you see they arent in that dungeosn gear or higher, and arent using CDs, dont even THINK about using a DPS move that doesnt stun, or else that tank will be dead before the cast of another heal finishes.
(most tanks cant survive 1 GCD, followed by the cast tiem of ur heal, even if they are at full HP. Sooner or later too many crits or DHs trigger at once, and suddenly they drop dead at full HP)
Once you're down to 3 enemies you can safely cast dmg spells, IF the tank is geared, using CDs, and is at full HP. (yes, even with 3 mobs, they still can die in a single GCD) once there is 2 mobs, you can rely on regen to do most of the healing, and almost stick solely to DPSing.)

in 8 man groups, most pugs just wing it, but I strongly suggest the healers pick "Main Healer" and "Off Healer" Where off healer focuses on AoE healing, and light helping of MT healing (mainly just on TBs.) And the Main healer focuses on keeping the MT healed, and lightly helps with AoE healing. (except on massive nearly party wipe raid dmg, then help a bit more)
This may seem stupid, but every time i get a pug group where healing just never seems to work, If I can convince the healers to pick roles, the group pretty much wins w/o a problem.