To equip or change a Spell, navigate to the Hero Inventory and select Spells, which is at the bottom of the screen under your hero. Select the Spell slot you want to change on the left side of the Spell screen.
A full list of all the Spells you've collected will be displayed in your Spell Vault on the right side of the screen, including Spells you've collected using your other Heroes, even if they are from a different Hero Class.
To change your Spell, select a Spell slot on your main Spell screen. Then select a Spell from your Vault that you'd like to replace it with and press the equip button.
You can also unequip a spell by selecting the unequip button which is under the spell currently equipped.
To compare a new Spell to your currently equipped Spell, select a Spell from the list on the right. This will bring up the equipped spell and show you the details of both Spells side by side.
Note: If you equip a Spell with a higher level than your Hero's level, the Spell will only have the effects as if it were the same level as your Hero.
While this Poison Spirit spell is Level 20, if I was to equip it to my Level 19 Hero, then a yellow down arrow will appear next to the Spell's Element icon and it will display as a level 19 Spell when you view it on your level 19 Hero.