Depends on the item.
Here are the rules for Spellbind:
Spellbinding
Spellbinding is a trait that some objects have (usually equipment spells). This trait allows you to attach a spell card to the object.
When you cast a spell with the Spellbind trait, you may immediately bind a spell to it. You can choose any spell from your spellbook that fulfills the limitations on the Spellbind object. For example, the Mage Wand can only bind an incantation spell, so you could not bind an attack spell or enchantment to it. Place the bound spell face down under the Spellbind object.
The bound spell can be cast as if it was one of the spells you prepared during the Planning Phase. You may only cast it once per round. When you cast the bound spell, reveal the spell to your opponent, and thereafter leave it face up and partially exposed from underneath the object it is bound to. You must use the appropriate action to cast the spell, pay the full mana cost, and check range, target, and LoS, just like normal.
If you use a bound incantation or attack spell, it is not discarded after casting. The Spellbind object retains the bound spell so you can use it over and over again in future game rounds. Also, if the spell is countered or canceled it is not discarded and remains bound.
If the Spellbind object is destroyed, any spell bound to it is also destroyed. If an equipment spell with Spellbind is returned to your spellbook (if it is replaced by another equipment spell, for instance), the bound spell also returns to your spellbook. Some Spellbind objects allow you to change the bound spell to a different one. The old spell is returned to your spellbook.
So when you cast the thing with spellbind, you choose and bind your spell. The rules don't say anything about paying a cost, so that's free unless the card says otherwise as a limitation (none yet do so).
Some objects with the Spellbind trait let you change what spell is bound. [mwcard=MW1Q19] Mage Wand[/mwcard] and [mwcard=MW1Q08] Elemental Wand[/mwcard] let you change the bound spell as a Quick Spell for 3 mana. [mwcard=MWSTX1CKJ02] Wizard's Tower[/mwcard] lets you change it for no mana or action cost during the planning phase. [mwcard=FWC16] Thoughtspore[/mwcard] doesn't let you change it at all, at any price.