Editor's note: this post will change over time, as people wiser than me add their ten cents.
Alphas:
Don't contradict them in front of other people. Request a private meeting and contradict them there. Then the alpha knows that you are loyal and honest. Also save the technical/detail problems for the bravo(s) wherever possible.
Bravos:
Don't get between them and their alpha in any capacity. Don't ask them to contradict their alpha, don't disrespect their alpha in their presence. Bravos are known for their loyalty, and if you get between them and their alpha, you'll find that out in a hurry. Also, you can use them to run problems up the food chain to the alpha. Like alphas, save the contradictions for a private meeting.
Deltas:
Request and respect their input. They know what they're talking about. Be sure to acknowledge their input and praise their work, ideally in public, but at the very least in private.
Gammas: Make sure interactions are in-person, with witnesses. Avoid anything you can't publish or at least document. Points 2, 3, and 5 of the SJW attack survival guide apply to everything you do with gammas: don't try to reason, don't apologize, and document everything. And keep them away from the women. They are stupidly high maintenance and probably best avoided.
Omegas: Remote work
Sigmas: Let them do their thing, because that's what they're going to do anyway. Ignore their various eccentricities and focus on that which is relevant to the work. The few I've interacted with appreciated the personal space. They're remarkably rare so not really worth worrying about.
Lambdas: Rare. If they're really open about their proclivities, see gamma. If not, see delta.