Before anything, welcome to healing! \o/

To keep the parties up, the most important is not to let the tank drops. He don't need to be always topped, but make sure that he always have regen on after the pull. DPS'es normally only need some regen from time to time unless they miss a mechanic. In this case, a Regen/Medica II normally would be enough to top them again.

And don't save swiftcast just for ressing. Swiftcast holy is great for buying some time to heal the tank when he overpulled. Swiftcast Cure II is great when you need a quick heal and Tetra is on cooldown.

And don't be shy to use Assize. The only wrong way to use it is when it isn't on cooldown. Try to stay near the tank to do an AoE attack that's stronger than Holy but also heals everyone near AND recovers 10% of your MP. It's... Magic!

And take Cure 1 off your bar. You don't need it (unless you're healing leveling roulette, where it can give you some dungeon under level 30).