In the Party interface, tap the space between the Servant portrait and the Servant's stats to select a Craft Essence to equip on that Servant. Craft Essences are maintained per party, so you can have the same Servant with a different Craft Essence equipped in multiple parties, or vice versa. Changing the Servant in a slot will automatically move the Craft Essence to the new Servant.
Equipping a Craft Essence confers a bonus of HP, ATK, or both, as well as an additional, special effect. The effect can be as simple as increasing damage dealt or decreasing damage taken, but they may also have a more interesting effect. In addition to boosting the Servant's stats, Craft Essences also increase its cost; the rarer the Craft, the more cost increases.
Craft Essences have levels just like Servants, and they are similarly leveled by using up other Craft Essences to strengthen one, increasing its bonus stats. It is possible to Limit Break a Craft Essence's maximum level up to 4 times by merging the exact same Craft in a synthesis; when you are selecting Crafts to merge, the same Crafts are highlighted with the yellow text seen on the right to alert you that you can Limit Break by merging that Craft. After the fourth and final Limit Break, the Craft Essence's special effect is increased; for example, 1★ Craft Essences that provide a 3% boost will now grant a 5% boost. Refer to individual Craft Essence pages for stats and special effects.