Must... fight... urge...
to engage Ilya Somin in lengthy debate on federalism in Star Trek. (Via Amber Taylor. Much too much to do, yet urge is strangely strong...
But I will suggest that the arrangement is probably confederal rather than federal-- there's no case I can think of in which the UFP legislated in a way that reached directly onto the surface of the planets, as it were. The problem is that we see vanishingly little of the civilian-to-civilian interactions that would be needed to decide the case. It's hard to learn much about how confederal, federal, or centralized a system is by watching the activities of its centralized military...
Update: OK, one more thing. The comments thread at Volokh quickly spiraled into the old standbys of social-science-geekery-about-Star Trek-- the allegedly post-scarcity economy (unless you happen to be a dilithium miner) and foreign policy/ the Prime Directive. That's because Ilya gave a very quirky tongue-in-cheek resource-extraction account of what the UFP's internal structure was like, but partly because those are the things we know how to talk about. Ilya's actual question-- how, if at all, is the Federation federal?-- isn't a Prime Directive question, and is only very indirectly a latinum question...