Always pay attention to party members' hit points. You don't want to be in a situation where party members die and you could have saved them if you were paying attention.
Use keyboard shortcuts to heal people faster. One common method is using the Function keys to select party members and the number keys to cast your array of healing spells.
Become completely familiar with your entire healing arsenal so that you know exactly what spell to use in any given situation.
Don't burn through your mana too fast, use timely healing so that you don't waste mana from overhealing.
Prioritize your healing targets when things get rough - you will likely want to prioritize the tank above all other members.
Always try to learn and accept tips from others on becoming a better healer.