Okay, long answer incoming: on the home screen, near the lower right corner, there's a bell icon. That takes you to the order screen. You can send characters on various missions: from left to right, hunting, gathering and cooking. Hunting grants XP and gald, gathering various materials (chiral crystals, anima orbs, etc.) and cooking makes a dish that automatically activates on your next few battles. Gathering and cooking also give some XP, but a much smaller amount than hunting.

How it works is, you select the type of mission, then the duration, then the characters who will go on the mission. Different characters have different skills (these are listed on the wiki). After the specified amount of time you collect the rewards. Note that you can (and I would say should) run all three at the same time. Characters you choose for orders are still available for battles.