When a spell can be cast depends upon its type:
Enchantment and Hex spells can be cast during the Conjuration sub-phase of your Strategy phase.
Conveyance spells can be cast at any point during the Remaining Moves sub-phase of your Movement phase.
Magic Missiles and Magical Vortex spells can be cast when a Wizard is chosen during your Shooting phase.
Assailment spells can be cast when a Wizard fights during any Combat phase.
A Wizard can only attempt to cast each of their spells once per turn. Wizards that are fleeing cannot cast spells. Unless stated otherwise, Wizards that are engaged in combat can only cast Assailment or range self spells.
To cast a spell, a Wizard declares which spell they wish to cast and its target (if required).