From what I understand you use your own personal aether and attune it to the stars that are aspected to the kind of effects you want to cast magic. Some stars are aspected to healing, so astros use their power to cast benefic. Others are attributed to destruction, and allow the user to cast malefic. The star globes represent the heavens and allow the user to align with the stars they want to draw magic from, much like how an Arcanist draws arcane patterns to manipulate aether.

As for the cards, they draw power from the constellations and grant effects based on the elemental alignment they represent. For example, fire is attributed to strength, so the Balance card draws that fire aspected aether from the constellation of the same name to boost the attack of the party.