Well, Captain Kirk goes out on the flagship and kicks some serious alien ass. Contrary to popular belief, he doesn't usually screw it, but he is almost contractually obligated to have his shirt torn. Spock bails him out with derisions of Something Something Diplomacy, I forget exactly what. And that's how the federation works. At a high level.
At a really high level, they all get zapped by plant spores and turn into hippies.