Psynergy
Psynergy is your magic, and you have a limited amount. When you walk around a dungeon or a place with monsters, your Psynergy Points will slowly recover. Be sure to keep a healthy amount ready in case it's needed to heal.
Djinni
There are two options for Djinn, Set and Standby. A common but risky strategy is to "Summon Rush" which is having all Djinn set to Standby before a battle. But having a Djinni on Standby is as good (or bad?) as not having the Djinni at all to boost your stats, so tread carefully with this strategy. Normally, cycling through Set Djinni can keep a balance of stats up so you won't have to be surprised when 1 hit KOs occur.
Know Your Order
This is useful sometimes. Know when each of your party members attack. Usually in Golden Sun, Ivan is the quickest. He would be best at healing sometimes when it's really needed. Mia is usually the one with a lot of healing skills, so pumping her agility will help a lot so you know who can be healed immediately.
Recognize Weaknesses/Resistances
All enemies have weaknesses and resistances, including your party. When a Psynergy of a certain element is used, you'll either see a !!!, !, or a . after the game calculates how much damage has been done. The triple exclamation mark shows that the attack was "super-effective". The single exclamation mark shows that the attack was "effective" while the single period shows that the attack didn't work well due to resistance. You can use this to your advantage when fighting enemies or bosses.