If your wondering how to use spells in Dungeon Inc first you have to own one, then lastly you can only use them during raids. Only 3 spells can be equipped before entering a raid so choose wisely. You can find a list of all spells here along with information on them. Lots of people online seem to think that spells are under powered and not very useful, though some of them are a must and can really help out during raids.
There are 2 places that you can get them that I know of. The first place would be the 5th day on the Daily Bonus Menu. Here you can get a chance at rare cards. The second place to buy them and with better choices would be the raid menu. Here you can spend keys on spells with the more rare one being more expensive. It’s a good idea to stock up on keys for purchase of the cheaper more useful magic cards. You can click on the cards twice before purchase to look at there stats. Be careful you don’t unintendedly buy a trap instead as they are also sold in the Raid store.
Dullerizer – Will lower the attack damage of the enemy. Good for getting past an enemy or to and helps keep your party alive.
Golden Arrow – This will do damage to enemies can can be good for extra damage.
Power Tapper – This card will raise the amount of damage done while tapping and enemy staff. Probably one of the most useful ones as it can help bring down a couple staff before your party can even touch them. The higher the cards is upgraded the better the stats. This one actually increases by a good amount with each upgrade. Luckily, this should be the first magic that you get in the game.