NOTE: I've posted an updated version of this article. I'm leaving this one up for comparison.
From the Rogue's Swashbuckle Talent: "Of course, 13th Age is a game where everyone might attempt stunts like this at some point. But you're the swashbuckler who is prone to automatically succeeding, often, instead of needing a difficult skill check to pull the stunt off."
As far as I can tell, the above quote is the only reference to a "stunt system" in the 13th Age core rules. Clearly improvisational "rulings" are intended to be used freely, though no guidance is given for how to make these rulings, particularly in combat. Here's my stab at it.
GM Note: If the players can make use of these maneuvers, intelligent monsters should do the same. You can use the homebrew rules for monster ability checks, or simply use the monster's attack bonuses.
Backgrounds: I lean toward not applying backgrounds to the skill checks
used during maneuver attempts. However, if you allow them where
appropriate, feel free to give monsters a relevant "background bonus" to
their PD or MD.
As a quick action make a Str or Dex check vs the opponent's PD. On a success the player can attack with a standard action, and on a natural even hit the target is tripped. On a natural odd miss, the target gets to make an opportunity attack. A tripped target is Stuck unless they spend a move action to stand up.
If the attacker wants to attempt a particularly nasty trip (bring the target down hard, or onto difficult terrain) it will require a little more precision, and/or the target will be trying harder to avoid being tripped. Instead of a natural even hit, the trip triggers on a natural 16+. In addition to being Stuck, attacks against the prone foe gain a +2 bonus to hit.
If the trip is attempted using a standard action then it automatically triggers if the skill check is successful, and it is considered a hard trip (target is Stuck and attacks against it get a +2 bonus).
SAND IN THE EYES
As a quick action make a Dex check vs the opponent's PD. On a success the player can attack with a standard action, and on a natural even hit the target is Dazed. On a natural odd miss, the target can make an opportunity attack.
This can obviously only be attempted if there is a suitable substrate for throwing in your opponent's eyes (sand, mud, ash from a campfire).
If attempted as a standard action the target is automatically Dazed with a successful skill check, and there is no danger of triggering opportunity attacks.
This is a catch-all maneuver for things like throwing chairs at enemies, pulling the rug out from under them, or dropping a tapestry, chandelier, brazier, etc. onto them.
Usually this will be used as a standard action, instead of attacking. It may affect one enemy, or 1d3 enemies in a group depending on the action being attempted. Make an appropriate skill check using the "Skill Check DCs, Trap/Obstacle Attacks and Impromptu Damage by Environment" table to determine the DC and damage based on the environment. Cut the damage in half if the effect inflicts some sort of status effect. Usually this will be Dazed or Stuck (if you're knocking the target down), though you could also use the homebrew rules for slowed creatures (if the target uses a Move action, roll a save, usually 11+, to see if they reach their destination).
As a quick action make a Str or Dex check vs the opponent's PD. On a success the player can attack with a standard action, and on a natural even hit the target is disarmed. On a natural odd miss the target gets to make an opportunity attack. Picking up the weapon requires a move action. If you roll a natural 20 after making a disarm check, the weapon is flung out of reach and the target will need to move to the weapon before using another move action to pick it up.
Use the Puny Grabs rule. You can use a quick action to grab a creature (Str or Dex vs PD), and on a success they take a -2 penalty to Disengage checks. You must have at least one free hand to grab.
As a quick action make a Str check vs the opponent's PD. On a success the player can attack with a standard action, and on a natural even hit the target is pushed back a few feet (it pops free of any engagements except the bull-rusher).
On a natural odd miss, the target can make an attack of opportunity.
If the target is being pushed into dangerous terrain (off of a cliff or into a campfire) that it is aware of, it is likely to defend itself against the bull rush that much harder. The bull rush is triggered on a natural 16+ instead of a natural even hit.
If attempted as a standard action, the bull rush automatically triggers if the Str check is successful and there is no risk of taking opportunity attacks.
As a quick action make a Cha check vs the opponent's MD. On a success the target takes a -2 penalty to attacks against anyone but you. On a failure the target is enraged by your taunting and enjoys a +2 bonus to attacks against you.
If the player spouts some really impressive taunts, or if the target has some narrative reason to react strongly to taunting, feel free to increase the penalties (and bonuses) to -/+ 4.
Depending on the nature of the trick, use a quick action to make a Cha, Int, or Dex check vs MD. Use MD+5 if the trick is stupid ("look behind you, an owlbear!") Usually on a success you can grant yourself or an ally a +2 bonus to their next attack against the target, but feel free to adjust this bonus based on what is being attempted.
Most enemies don't like being duped. What will prevent players from abusing this? Get creative, but for starters monsters should start gunning for the trickster. Also, most enemies won't let themselves be tricked twice, so this will usually be effectively a 1/battle thing anyways.