The Puddle rules can be found here. The game is a PDF file that's four pages long. It is free.
As a brief summary, each character sheet has six traits. These can be, really, as broad or narrow as needed. They are whatever is important to the character, and need not describe competence. The traits guide narration. They also have a mechanical effect I'll say below.
Each player starts each game with six dice. They get to choose how many dice they roll for any given situation. There is a 1/3rd chance that they will lose a die when they roll it; so rolling more dice tends to give a better outcome but a player also tends to lose more dice this way. If they have a trait -- any trait -- that is applicable to the situation, they get a die (not for that particular roll, but for their dice pool). So, yes, if a person is "the world's greatest swordman" they get a die just as if they were "the world's most incompetent swordsman".
The dice rolling give six general results: failure that is narrated by the GM, a neutral outcome that is narrated by the GM, a positive outcome narrated by the GM, a positive outcome narrated by the player and a positive outcome narrated by the player during which they can add or modify a trait. Generally, players get a positive outcome narrated by the GM. It's about tied for failures and outcomes narrated by the players. Adding traits is pretty rare. Neutral results are by far and away the rarest outcome of all.
To make a few more things clear: the GM does no dice rolling. The GM has no character sheets, tho' often I have notes that describe what I think a character is. But more on that sort of thing below.
When narrating, the trait used in the contest must be brought into play.
Example #1. The scenario is the Iron Enforcer, an ex-cop thrown off the GCPD for brutality combined with incorruptibility who now delivers street justice, is scouting out a warehouse where a drug deal is going to go down. I, the GM, know that there's a sniper who is covering the area looking to kill one of the PCs. I give the Enforcer a roll.
The player gets to narrate the outcome! So I ask the player what his character sees. The player says he notices an on-duty uniformed cop guarding the drug warehouse.
That on-duty uniformed cop did not exist until the player put him there. Now, I've got to roll with this punch.
Ironically, the Enforcer does not notice the sniper! If the player had said, instead of putting that cop at the gate, that "he sees anything of importance that is hidden" then I would have told him about the sniper, but he did nothing of the sort, chosing to add the cop.
Example #2: Remember that sniper? Well, since the Enforcer didn't see him, he enters the warehouse. I say, "Someone is shooting at the Enforcer. You need to make a roll." The player says, "Can I use my trait of Tough As Nails, here?" I go, "Yes" and hand the player a die. He makes the roll: successful but the GM narrates. I say that the Iron Enforcer is shot through the rib cage but he's so tough that this wound -- which would be nigh crippling for another person -- is only a slight inconvenience for the Iron Enforcer. He still gets under cover.
Example #3: Sariel, a religious fanatic who believes she is on a divine mission to destroy evil, and who has a pair of flaming katars and is a trained assassin, is fighting Graceful Liang-xu, a great martial artist . . . but the player gets to narrate. The player says, "Liang-xu's reputation is exaggerated; she's actually a push-over. Sariel just shatters Liang-xu's sword with her blades and Liang-xu falls down begging for mercy."
Up until that point, Graceful Liang-xu had, in fact, been a great martial artist. But the player changed that. Which is the reason why NPCs in The Puddle do not have character sheets. At any time a player might seize narrative control and completely alter an NPC.
Example #4: Sariel is confronted by St. Dumas -- who is either a spirit or a sign of her mental instability, it has not been decided. St. Dumas tries to cow Sariel. There's a roll and the player gets narrative control and gets to add a trait. She describes how Sariel is utterly broken by the awesome presence of St. Dumas, and falls to the ground sobbing and begging for forgiveness. Yes, she decided to fail. Has I narrated a positive outcome I would have certainly had Sariel stand her ground against St. Dumas. She adds to her c-sheet, "Mindlessly follows St. Dumas's orders." Now, whenever she is following Dumas's orders, yep, she'll get a die.
Example #5: Gibril -- an amnesiac Lexcorp cyborg that can move at incredible speed -- is having a rocket fired in his direction. He wants to avoid it by running out of the way of the explosion, an obvious application of his super-speed. He gets a die. But he fails the roll! I narrate that he doesn't notice the rocket coming until it's too late -- he is close to the point of the blast and is thrown to the ground where his cybernetics are badly damaged and his right arm is broken. I say he is also dazed as his cyborg body reboots in safe mode.
Example #6: Gibril, who has Smooth Talker as a trait, is trying to get the techno-ninja Xu'Fasch to bond over their respective kung-fu skills. He rolls and and the GM narrates a positive outcome. I, the GM, put words in Gibril's mouth as he talks with Xu'Fasch about their shared martial arts experiences and how Xu'Fasch appreciates Gibril's masters and skills. Yes, the GM took the character over to resolve the social outcome.
Which, I think, is enough examples to demonstrate -- briefly -- how the game differs from traditional RPGs.