In particular, how their military forces are integrated.
AFAIK, it's the DS9 episode "Rapture" which first suggests that a new member world's military forces will be absorbed into Starfleet. It doesn't say exactly how they do this, although I'm sure that it's a simple matter of their officers receiving some kind of Starfleet training, after which they receive Starfleet ranks equivalent to what they had (for instance, after Bajor joined the Federation, COLONEL Kira of the Bajoran Militia became CAPTAIN Kira of Starfleet).
About a new member not necessarily having a global government: I don't think that's possible, as one of the (few) requirements for Federation membership is that a world MUST have a single global government. (TNG's "Attached")