There's a neat guide that goes through the different concept of the arenas here~
In addition to the information there, arena scores are based on:
If you deal the last hit on a player from the opposite team, it will count as your kill.
Dying reduces your points.
Total amount of damage deal on the crystal(s.)
Total amount of damage dealt on players on the opposite team.
Amount of HP you restored to yourself and to other people on your team. HP pots also count to your treatment amount.
I think that covers the basics at least~