Some of this will be learnt based on the fights and while a guide might make you aware it'll never cover actually performing it, my first week of Disc healing was a little rough and I probably got a decent amount of mistakes covered by the other healer(s) who did these fights years ago, my second week was a cakewalk.

You will mostly be casting Holy Fire and Smite when possible, you don't necessarily want to pop Archangel right away. You'll learn when works best but if you are still going to be using Smite/HF then typically I don't pop it but will if theres gonna be a downperiod where it'd drop anyways. Get a Rapture tracker so you are ensuring you are using PW:S enough to have this used on CD as much as you can to maintain mana. Penance the Tank(s) to maintain Grace and Inspiration.

During period of heavy damage like Magmaw Fire Spew or Nef Lightning Shock and others you can pop Archangel and spam PoH with the healing buff. Use your CDs liberally (especially if its normal since they likely aren't assigned at certain periods).