Use a jade in your item menu to activate it and call its Fairy out, or to recall a fairy that is already out. You can have two jades active at any given time. After you buy or find a jade, you cannot later sell it, though you can discard it if you desperately need inventory space.
Several jades can be bought from the man on the far right room at the top floor of the Inn. The rest are found in dungeons.
Fairies level up by collecting the little blue energy crystals that enemies rarely drop. Each crystal is worth 50 XP and most fairies take 2-4 crystals per level. The first fairy to grab the crystal gets the XP, so slow ones might never beat faster ones to the XP.
If you're desperate to level them up, go in the southeastern door just inside the technological part of the Ancient Ruins and continue through to the dark room with the light switch, the two floating panels, and the sea of electric tiles. One of the blue enemies there will always drop an energy crystal so you can level your fairies up as much as you want.