So to add on what others have said:

Healing in general: Get a good feel for the "chunk" of the HP bar each heal can do (if you are a numbers person you can go that route too). You'll get a feel of what each heal can do and if it will overheal or not.

Don't be reliant on your Benefic II spell. Unless the target is going to die if they do not get another heal right after, your Benefic I heal will do great and save MP. That being said, if their HP bar is going down quickly, go ahead and use II !

Make sure your gear is up to snuff. Even moreso than a tank, you need to make sure you can recover from those big hits.

For AST in particular:

I wouldn't worry too much about the cards when first starting out. If you can apply the cards to the right person, great. Heal first, DPS if you feel comfortable, and cards are last when starting. Once you get into a groove, you can balance all three parts.