To use magic in New World, you will need to level up your intelligence or focus attribute and pick a weapon such as fire staff, life focus staff, and ice gauntlet.
Using one of these three weapons is the only way to use magic in New World, as the game doesn't have any spell casting or any magic system beyond these weapons.
That said, if you want to use either the fire staff or ice gauntlet, you will need to level up your intelligence attribute and get your hands on the weapon through looting, crafting, trade store.
Related: How to craft Gunpowder in New World?
Once you got either the fire staff or ice gauntlet, you will be able to use magic-like abilities after you level up the weapon mastery for either weapon. However, if you don't know how to level up weapon masteries, you can do so by using the weapon to kill enemies, so the best way to level them up is to do quests and just play the game.
Eventually, you'll start to level up and earn weapon mastery points, which can then be used to unlock magical abilities for both the fire staff, and ice gauntlet in New World. The same also applies to the life staff, but you will need to level up your focus attribute to use the life staff.
Check out some of our other guides for New World!