They never explain what happens with things that are still scarce. There are several episodes where mention is made of valuable artworks. Peoples time is still scarce, for example holodeck programs take time to create. Starships are clearly not free, and therefore neither is interstellar transport.
Like much of the Star Trek universe, it seems that the writers threw in a neat idea and never gave it much thought.
We do know that Federation citizens use non-Federation currencies. Barter seems to be reasonably common in the Star Trek canon.
My own theory is that the goods that are still scarce are utterly trivial, like Beanie Babies or Pogs circa 2018. Everything that you might reasonably want or need is completely free within the Federation; a handful of eccentrics might covet a rare painting or an antique, but the vast majority of people would see their preoccupation as absurd. A lay person might admire a rare painting, but they would see no reason to steal it.
I also think that Federation culture plays a significant role. It's clear that greed of any kind is seen as primitive and antisocial by the overwhelming majority of Federation citizens. We could draw parallels with the Amish or Mennonites - you can't have status goods in a society where displays of wealth actively lower your social status. The Federation is not just a post-scarcity economy, but a post-scarcity culture.
We could think of the time investment in things like holosuite programs as being loosely equivalent to the philanthropic activities of the very wealthy circa 2018, conferring no material benefit but a substantial degree of social capital. Designing a hit holosuite program might not earn you any money, but it would get you an invite to the Federation equivalent of TED. Joseph Sisko charges nothing for meals at his creole restaurant, but earns the respect of his neighbours.
This is a fascinating article speculating on the mechanics of the Federation economy:
We do know remarkably few things about life on Earth or a developed colony. On a starship you have duties, you work, and people are discriminated according to military rank (better living quarters, more holodeck privileges). But what do people do on Earth? If there is no money and instead civilian egalitarism what or who decides who lives in a mansion on the beach or a small city appartment? How does Picards brother „own“ the family vineyard? And what do people do with their life? Is there a 5 hour work week?
> If there is no money and instead civilian egalitarism what or who decides who lives in a mansion on the beach or a small city appartment? How does Picards brother „own“ the family vineyard?
The usual answer when this question is raised is either "they inherited the land" or "a committee decided the the Picards were the best for tending the vineyard".
Not 100% convincing to me but there is no better answer AFAIK.
> And what do people do with their life? Is there a 5 hour work week?
That one is easy, though. Let me quote Jean-Luc Picard: "The acquisition of wealth is no longer the driving force in our lives. We work to better ourselves and the rest of humanity."
Like much of the Star Trek universe, it seems that the writers threw in a neat idea and never gave it much thought.