The various quests are the best way to get experience points in Wartune. Make sure you use your Stamina to complete your campaign quests. Go through all the daily quests that are available for you. And lastly do not forget to do the Wartune Bounty quests. By putting your focus with the quests, you should find yourself leveling 1~2 levels a day.
I want to put a focus on the Wartune Bounty quest because you should aim to get orange Bounty quests. Bounty quests are fairly easy to accomplish in Wartune. A single Orange Bounty quest worth 4 times exp than the regular white one.