The diceless system I have experience with is Amber. Basically you establish some background and areas of capability for the character. The GM explains what the character’s senses and history tell them. The player says what they want the character to attempt and the GM describes the result based on a) the character’s abilities, especially in relation to other characters, b) established canon in the story c) what makes the most satisfying story for the greatest number of players.
This requires TOTAL trust in the GM and like most RPGs requires the GM to adjudicate most of what happens. The useful rider we have discovered is that players can interact on their own if they respect the canon and are doing things that don’t affect the overall story for other people.
The trick is knowing when you absolutely have to get the input rom the GMs.
This is why in the bar etc. I try to keep all the things I make up on the fly a) reasonable for the character b) low or no impact to the overall game c) try to offer the GM hooks and veto over anything based on anything the character does not know for sure.
That is why I would say “maybe” I know a guy. And then let the GM tell me if the person I am thinking of could do that or not, or perhaps a better way within the story to achieve what I was after. I try to create texture for the character that could be expanded or left alone.
System wise, this works pretty well using any character generation system. I happen to like GURPS. Not necessary the rules mechanics, but you can create cool and very varied characters and then just play diceless.
How do you decide if a character succeeds at doing something? You look at his capabilities. If it seems reasonable, you allow it. If their is a reason they cannot, then a cunning plan or careful approach, or gathering the right resource or shifting the field of conflict, can help to overcome the deficit.