One Roll: The Save
When your knave attempts something with an uncertain outcome and a price for failure, you make a saving throw — a save. Roll d20, add the relevant ability bonus, and beat 15. That is the entire engine; the full text, with the designer's math, lives in @Missing file.
A new knave succeeds about a quarter of the time. A level 10 knave, with bonuses as high as +10, succeeds about three-quarters of the time. In between those two facts is your career.
Opposed saves
When another creature actively resists, you are not trying to beat 15 — you are trying to beat their relevant defense. A defense is just a bonus plus ten, so it is the average of what they would roll.
A wizard hurls fire at a goblin. Resolve it either way: the wizard rolls d20 + Intelligence bonus against the goblin's Dexterity defense, or the goblin rolls d20 + Dexterity bonus against the wizard's Intelligence defense. The odds are identical.
Because the odds are the same no matter who rolls, the table can put all the dice on the players' side whenever it likes — your sheet even prints your defense roll, ready to go.
Advantage and disadvantage
When circumstances make a roll significantly easier or harder, the referee grants advantage or disadvantage: roll 2d20 and take the better or the worse die.
Which ability?
The table in Making a Knave covers the spread; when in doubt, describe what you're doing and the referee names the ability. Attacks are saves too — Strength for melee, Wisdom for ranged — covered in Combat. And remember the two abilities with day jobs: your Constitution defense sets your item slots, and your Charisma bonus caps your hirelings. The full breakdown is in @Missing file.
The best save is the one you never roll. Wedge the door, test the floor with the pole, pay the goblin. Dice are for when cleverness runs out.