I always found the idea of a world with no money to be utterly stupid. Otherwise, why even have a merit system? Or military rank/pay grade? Or, how do trade exists? Clearly, back in TOS, you had such characters as Harry Mudd and Cyrano Jones within the Federation who sought out profit. And there are non-Federation members to deal with, such as the Ferengi (thank goodness for gold-pressed latinum). Now, don't get me wrong. I like the idea that humans of the 24th century believe that perfecting one's self was a much noble proposition than the accumulation of wealth. I fine with that. But I think that the "there is no money in the 24th century" is just another case of GR trying to preach a kind of utopianism that doesn't take into account that greed, not money, is the problem. But, that's just me...
It's well illustrated in the series that privilege is a form of pay.
Captains get better access to everything.
Which is why everyone wants to be a captain in the universe.
Today most adults living in first world conditions value four things that come along with money.
Transport(Cars)
Real estate( Where they live)
Experience(travel, hearing fancy music, skydiving etc)
finally social exclusivity(special access to a place, fame, reptutation, befriending attractive or wondrous people etc.
In the star fleet universe all of these things seem to directly go along with rank.
Star ships are not unlimited, Access to unique places or even a big room on a star ship are coveted, most experiences can only be had through be an officer etc, and even who you meet is based on your rank.
So it'd be easy to see why there is no need for money.
We live in a world where money is used both as a way of managing demand and managing the usage of resources.
Everything we know about the trek universe suggest these two things are split, with demand being managed by merit(rank/position) and resources being managed by those in position/computers.
Picard was offered a position in turning the Mediterranean into land, sisco was offered a job in managing the construction of habitats in orbit. This theme goes on and on.
Resources are not unlimited, they're simply at a higher standard than we are use to.