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; however, if you swap 2 Servants who are both in the same party you will to have swap the equipped CEs manually.
Craft Essences give additional HP, ATK, or both, as well as a special effect. Effect range from simple (increasing damage dealt, decreasing damage taken) to complex (give the rest of the party effects when defeated). Craft Essences also have cost; the rarer the CE, the more cost is needed to equip.
Craft Essences have levels just like Servants, and they are similarly leveled, by feeding other Craft Essences to strengthen one, increasing its bonus stats. You can Limit Break a CE up to 4 times by merging the exact same Craft in a synthesis; when you are selecting Crafts to merge, the same Crafts have yellow text as seen on the right to denote a Limit Break is possible. This increases the CE's max level. When fully limit broken, the CE's special effect is enhanced; for example, 1★ CEs that provide a 3% boost will now grant a 5% boost. Refer to individual Craft Essence pages for stats and special effects.