In Tales of Radiance, your heroes do not gain experience points on their own. In order to power them up, you must manually level them up using hero XP (those green potions) and gold. To do this, simply go into your heroes and hold down the Lv. Up button to start leveling them up. If you want exact levels, you can just tap the button once. This is the main way of powering up your heroes, so do not forget to do it often! You get a lot of hero XP and gold every time you take down a boss, so do not hesitate to level up your heroes. If you are afraid of investing too many resources into low rarity heroes, don't be - you get all of those resources back very fast!