If you didn't live and grow up in the 20th/21st centuries, you would have no idea how the world economy works. I've always been satisfied to tell myself that the Federation economy is just too complex for me to understand. When Jake Sisko says Fed citizens don't have money, I take that to mean money as we know it.
A society, no matter how socialist, has to have currency to trade with other societies. There are things that cannot be replicated (time, energy, land, art) and ownership of them has to be determined somehow.
I can accept that the Federation is money-free. I can also accept that I have no idea what money-free actually means. One look at Trek tells me that I don't need to understand how it works, just that it does work.