How 'deep' do you want to go?

If you want to do EX primals, second coil, basically all the "hard" content FFXIV has to offer... learn the fight patterns really well. You need to be able to anticipate stuff happening and already be in motion or casting. Although out-of-game guides can help, a lot you'll only learn by doing.

As a practical matter, try solo healing some EX primals (say, titan and leviathan? Or to start off a bit easier, just garuda...). When you get that down, you're doing very well.

If you're just intending to play more casually... well. Make sure to avoid oneshot mechanics and such but pretty much just heal as the damage comes. Stoneskin on DPS and other healers during downtime. Regen on the tank or anyone tanking if you can spare the GCD. If you made it through Aurum Vale leveling up, you should be fine in any level 50 dungeon as long as you're geared for it. HM primals take a bit more dodging but they're still pretty easy.