As mentioned above, you can increase your casting throw DC by increasing your spellcasting ability’s modifier. You can level up and use items, but one difference is that you can also choose talents that contribute.
When maxed out, the only magic items that increase his casting DC are the Tome of Guidance and Influence (Very Rare), which increases her Charisma and Charisma Max by +2, and the Archmage’s Robe (Legendary, only for Walrocks, Wizards, and Sorcerers), increasing the casting check DC by 2.
Casting is calculated by adding your proficiency bonus and your spellcasting modifier for your class to eight. This total is the DC of the casting roll that the targets of your spells must meet or exceed in order to successfully save.
As with any spellcaster, your casting DC = 8 + your skill bonus + your ability modifier. In this case, your skill bonus at level 3 is +2 and your skill modifier is Wisdom. Your DC is the difficulty of the spells you cast. Example: With Wisdom 16 (+3), your casting throw DC is 13.
The maximum permanent casting DC possible is 28
Robe of the Archmage. Staff of the Pact Keeper (applies only to your Warlock spells)
To put it simply, a DC determines how hard something is to do. Whether it’s climbing a rope, dodging a breath weapon, or swinging an axe, different actions have different DCs. To determine if you beat a DC, you must roll equal to or higher than said DC.
Spell Rescue DCs opponents must roll to avoid your spell effects. When you cast a spell that requires a target to save, the DC is what it must roll (after adding its stat mod) to avoid or reduce the spell’s effect.
A skill check succeeds if the roll is greater than or equal to the task’s Difficulty Class (DC). Normally the dungeon master decides the DC. Sometimes the DC is determined by the result of a check by something else, this is an “opposite check”.
Your spell attack modifier is equal to your wisdom modifier + your competence bonus, which in this case is +4. This means when you cast a spell that requires a spell attack roll, roll a d20 and add 4.
The Skill Scores and Modifiers table lists the skill modifiers for the range of possible skill scores from 1 to 30. To determine an ability modifier without consulting the table, subtract 10 from the skill score, and then divide the total 2 (round down).
The casting DC calculation depends on where the spell came from. If you know the spell from the caster’s spell list, it would be 8 + skill bonus + intelligence modifier. However, if you know the spell from the sorcerer spell list, the casting check DC would be 8 + skill bonus + Charisma modifier.