All of the Star Trek series of the '90s/'00s overlapped quite a bit (in writers/universe/stories/cast) and some of the later ones fill in some of those missing details.
The Federation has a currency, "Federation credits" -- they discuss a deal priced in credits for control of the Barzan wormhole, and Federation crew use these credits to make purchases at the Ferengi-run bar on Deep Space 9. The Ferengi keep all their wealth in the form of latinum, precisely because it can't be replicated. Presumably the only reason they need these credits is to facilitate trade between species; I don't remember them ever discussing how the crew get the credits.
The replicators' energy comes from the ship's warp engine, the same thing that powers everything else, and from recycled material. They can both convert matter to energy and energy to matter. We know they use the ship's energy because when Voyager is stranded with limited fuel, the first thing the captain does is ration replicator usage by the crew, and pick up a chef to start cooking fresh food instead of replicating meals. The energy source for the engine, in turn, was controlled annihilation of matter (deuterium) and antimatter (anti-deuterium). The ships all had Bussard ramscoops with which to collect deuterium from interstellar space for use as fuel -- that was the red part on the front of the nacelles on the Enterprise D in TNG for example.
In an episode of ST:DS9, they discuss the fact that the Federation does restrict the ability to replicate dangerous objects like weapons without authorization. Trade in weapons is always implied to be heavily regulated.
All that said, most of it is really left to our imaginations. I was hoping Star Trek: Enterprise, the prequel to the rest of the series, would shed some light. Unfortunately it wasted 3/4 of its time on weird time travel plots that could've taken place in any of the series, and only tried to get back to explaining how the Federation came about at the very end... just before being cancelled.
The Federation has a currency, "Federation credits" -- they discuss a deal priced in credits for control of the Barzan wormhole, and Federation crew use these credits to make purchases at the Ferengi-run bar on Deep Space 9. The Ferengi keep all their wealth in the form of latinum, precisely because it can't be replicated. Presumably the only reason they need these credits is to facilitate trade between species; I don't remember them ever discussing how the crew get the credits.
The replicators' energy comes from the ship's warp engine, the same thing that powers everything else, and from recycled material. They can both convert matter to energy and energy to matter. We know they use the ship's energy because when Voyager is stranded with limited fuel, the first thing the captain does is ration replicator usage by the crew, and pick up a chef to start cooking fresh food instead of replicating meals. The energy source for the engine, in turn, was controlled annihilation of matter (deuterium) and antimatter (anti-deuterium). The ships all had Bussard ramscoops with which to collect deuterium from interstellar space for use as fuel -- that was the red part on the front of the nacelles on the Enterprise D in TNG for example.
In an episode of ST:DS9, they discuss the fact that the Federation does restrict the ability to replicate dangerous objects like weapons without authorization. Trade in weapons is always implied to be heavily regulated.
All that said, most of it is really left to our imaginations. I was hoping Star Trek: Enterprise, the prequel to the rest of the series, would shed some light. Unfortunately it wasted 3/4 of its time on weird time travel plots that could've taken place in any of the series, and only tried to get back to explaining how the Federation came about at the very end... just before being cancelled.