The other problem with a moneyless society, is how were people compensated when their cash, property, products, farm goods, and stock certificates suddenly became worthless.
1) Credit. Everything is done on a evolved form of credit. The more you work, the more credit you get. It's all electronic with no real value outside the system. Sure there's an exchange rate, but outside the Federation/Earth you're not going to get as much as you would back home.
2) Energy/Replicator "Credit". You're guaranteed a basic level of living whether you work or not: A place to live (apartments/dorms), food, clothing, medical care, etc. But if you want better you need to work to earn the "Credits" to replicate bigger and better things. Example: Everyone may have a good, basic, sturdy communicator, but if you want a I-Communicator 5s you need to earn the replicator credits to replicate the device. Everyone might be entitled to a PADD but if you want the latest and greatest from Rigel III, you gotta earn the credits.
Or it could be some combination of the two.