I'm levelling WHM to cap atm as it is my last 50, Since I have seen every dungeon hundreds of times before, I already know where the large or more dangerous pulls are so it is already immediately easier to heal when you know how much damage the tank is likely to take, which allows you to maximise DPS in cleric stance before switching back to heal. I generally start every pull in cleric stance (Tank has full hp at this point anyway) and stick Aero on all the enemies, if it is a large pull I will switch earlier and begin healing, most 3 enemy packs and a reasonable tank (better geared tanks will give you more time to cast Stone for extra dps, worse geared less time) Some dungeons have groups of 4 or adds roaming (or ones that hit VERY hard) so you should be prepared to heal quickly should their hp drop, if you have already been through all the dungeons before and can remember these things your job is instantly already much easier, if not then don't try and over DPS on a pull you aren't sure on or haven't seen before because it could be the one your tank dies on.
I always check the Tank's gear before the start of the dungeon, if they are wearing any Disciple of War equipment or even DRG/WAR/PLD equipment you can already assume their defence will be lesser than that of a properly geared tank for that level and will require additional healing (underleveled gear also contributes, accessories aren't a big issue during 1-49 and the dungeon appropriate green gear is the best, failing that a level synced high level tank will be very well geared too this all decides how much DPS you can expect to get out of a dungeon before having to take care of the tank, some tanks you will have to babysit the whole run) the tank's skill on maintaining enmity on all enemies will also decide on how you can approach the dungeon. It is little point DPSing the enemies if you are only going to tear the hate of a tank who doesn't use overpower and/or flash and everyone is running around chasing enemies. If you do accidentally pull hate DO NOT run around (except in the case of Cutters cry first boss where your job IS to run around with all the ants on you), run TOWARDS the tank and stand still, it is easiest and quickest for them to get it back off you that way and if the DPS are attacking it do not need to chase it down either, also in this case DO NOT use Fluid Aura (you can use it on some bosses where there is no pushback but I don't have any specifics on which ones so personally I don't really use it at all unless I am soloing) as there is nothing more annoying for a melee DPS or tank to have to chase the enemy you just sent flying away.
These are things I have picked up on levelling all the other jobs to 50 that I notice. People who have posted before me will provide better information on rotations and skill usage as they are likely full time WHM's as opposed to my measly level 45.