From what we've been told, at least by the 23rd century, there's no money. So I would guess that everyone gets a baseline "basic" resources. Although, if every home has a replicator in it, what else would United Earth/Federation have to supply beyond power (and The Voyage Home says it's all solar based)? A replicator would take care of food, clothing, and all basic necessities.
Well, you'd still need
some additional services. Houses and infrastructure would still need (periodic) maintenance, for example. The average citizen's replicator probably cannot fix their crumbling houses if that were to be absent.
In The Wrath of Khan, during the scene where Spock presents Kirk with a copy of A Tale of Two Cities and discuss his birthday at Starfleet Academy, there's a guy in the background cleaning the floor. And I've always tried to match that with everything we've been told about Earth and the Federation.
Why would a person want to do a job cleaning floors in a money-less society that has done away with greed if they don't have to? Because, even if you take Picard's words from First Contact at face value, polishing linoleum doesn't exactly fit with doing work that's bettering yourself and the rest of humanity. Maybe in a society where people's basic needs are taken care of, that guy is satisfied and happy cleaning floors, and goes home every day to replicate synthehol. The feeling I've always gotten is that a restaurant like Joseph Sisko's exists for anyone to come in and eat. Sisko's father runs it because he enjoys being a cook and cooking for others. And that's how public services exist. In Star Trek's Earth, people work and provide services out of the mutual joy it provides them to perform a function.
Simple work in itself can be quite satisfying. Most of the frustrations I've had with doing (relatively) simple work didn't have to do with the work itself, but with how people
treat you based on your role. For example, I've done both vocational and Ph.D. level jobs, and I was taken aback by how differently I was treated, even by the
very same people in the same company. Some people excercise all their needs for 'development' within their line of work; others find their expression more outside it and are content to do simple work even if they could do something 'far better'.
But beyond that, how exactly is property transferred in that kind of society? Like do the Siskos "own" their restaurant? Can they "sell" it to someone else? But if you have no currency, how do you buy or sell it? Unless a Ferengi comes along with latinum, is Earth back to the barter system if you want to transfer goods?
It's why I always have refused to believe the Federation has no money. In my view, it's quite
impossible to run any sufficiently advanced economy without it. The only explanation I could accept is they invented something
beyond money, something better even to handle those kind of needs. But a simple barter system sure as hell it can't be. Money was invented because of the considerable drawbacks of the barter system in the first place. (Well, and to get rid of the hassle of having to determine the purity and weight of every slice of gold or silver that was used in trade, and just refer to a centralised authority (e.g. the king of that reason) that vouched for the value of that piece of gold).
I'll add to that that I'll call
any kind of abstracted 'credit' system that can be exchanged for certain (limited) goods 'money', even if
they don't. I've always thought it was beyond dumb to have them declare the Federation no longer used money. All they'd needed to do was to declare they still had money, but nobody was interested in it in any other way anymore than as just a means to facilitate fair transactions.
Limited goods there'll always be. Take for example Data in
All Good Things holding the Lucasian Chair and living in the original Newton house. Even if others could duplicate the exact house, only Data gets to live in
the actual Newton house (as long as he holds that chair, at least). Same for, say, original van Goghs, even though there may be billions of replicated copies floating around.