There are several ways you can earn Experience for your character. It is mainly gained from completing missions, adventures, and patrol activities. Experience can also be earned from eliminating enemies, the more powerful the enemy the higher your Experience reward. Listed below are best ways to get Experience.
Red War Campaign Missions
Not only will these missions reward you with plenty of Experience when completed they also unlock new areas to explore along with new activities and items that will increase your Power Level.
Complete Adventures
Playing the Adventure missions that are scattered around each world as you progress through the game is another way you can earn Experience. A lot of these Adventure missions are geared towards lower-level players and wil have power requirement that should be somewhere alongside the one you obtain by completing Campaign missions. They will also reward Guardians with Rare equipment which may be a significant improvement on your current loadout.
Loop Heroic Public Events
Another good way to earn Experience is to repeatedly play Public Events while exploring the four planets. If you trigger the Heroic modifier on each event you play you will gain extra Experience along with a chance of getting better item drops.