You can't "join" the Confederation, but there are a few major mission series you can do for them. You need a high combat rating and must have a good legal status in Confed systems to get the more advanced missions. If you want a hint at what the further Confed missions are like, read below, but even a small description might be spoiling it for you if you like discovering things for yourself.
All but the last Confed mission series begins at a random planet. The first two mission strings offered by the Confederation are relatively short. One involves destroying a Rebel prototype ship called the Escort Carrier. The other is a simple recon mission for the Confed fleet. A larger and more difficult string involves a Rebel raid on the planet Ruby in which a classified weapon is captured. The Confederation hires you to retrieve it from the Rebels. The last mission string, and the most difficult, begins at Hogdon's world (I might be wrong, it's been a while). You'll find out in due time what that string has in store. Good luck, spacer.
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-Peregrine
"The people that once bestowed commands,
consulships, legions, and all else,
now concern themselves no more, and longs
eagerly for just two things: bread and circues!"-Juvenal
"A little science estranges a man from God.
A lot of science brings him back."-Francis Bacon