Theres some guides on the guide section if you look but the basics.
Shadows can be equipped like equipment. You unlock slots to equip them at 30+. You can only equip 1 of the same type of shadow (HP, Attack, Dodge, etc) at a time.
Shadows are levelled by feeding weaker shadows or shadows with lower XP to stronger shadows. A shadow can only eat a type lower than it (S can eat A, A cannot eat S) and can only eat a shadow with less exp then it (a 50k exp shadow can eat a 25k but not the other way around).
There are currently 7 kinds of shadow demons available: Critical Hit Shadow Demon, Hit Shadow Demon, Dodge Demon, Physical Attack Shadow Demon, Magical Attack Shadow Demon, Speed Shadow Demon and HP Shadow Demon.