I gamed this out for a writing project a while back. I think that doing it openly with economic domination would be the most effective way. You can look at how third world countries have become subordinated to major powers solely through making deals that seem to make things better for them. Or even how major powers' citizens have allowed their leaders to develop alliances that undermine their sovereignty, and kill their jobs and ways of life in exchange for cheap foreign goods.

As long as aliens have something to offer Earth, I think a lot of our leaders would easily sell us out in exchange for nice things in the short term. Humans would fight over who really had the right to make a deal with aliens, while our boldest governments and individuals would just go ahead and do it. You'd be looking at a loud, peaceful "first contact," followed by a bunch of starry-eyed rhetoric about moving forward to the future, growing into an interstellar community, etc. In the end ordinary people would have little control over Earth's relationship with aliens, and in return the aliens would be able to do just about whatever they wanted, since they'd have most of the cards (assuming their tech level is far beyond ours).

With an understanding of human cultures, it would also be pretty easy to manipulate public opinion. Conservatives could be manipulated with appeals to renewed power/sway to one's country through cooperation with the aliens. People delude themselves into thinking they're more important than they really are, that they'd be equal partners, or that they'd be the ones exploiting the aliens. Liberals could be manipulated with appeals to social justice. Just like corporations use milquetoast social issues rhetoric as a shield against whatever bullshit they're up to, the alien/pro-alien faction could attach itself to some idea of progress, improvement of human society, etc. And anyone who wanted things to go back would be painted as a regressive.

Edit: I'm not going to argue with you about IQ or whatever, but it's worth remembering that third world countries are often pretty good at shitting all over open occupiers and invaders. People with inflated ideas about their own sense of civilization are easier to manipulate. Third worlders would start shooting/bombing a lot sooner, and if they couldn't win many would burn their country to the ground before giving it up to invaders.