Economic: They've the wealth to buy influence and dominate the media to spread propaganda. Buying banks and industry so they can leverage whole cities and politicians. Like the DeBiers diamond cartel: They can outspend and financially bury anyone who won't play ball.
Technological: They've got a hammerlock on something new and wonderful that everyone simply feels they must have. Cheap but advanced energy/gas alternatives, nanotech miracle medicines.... great stuff, infrastructure comes to depend on that technology, which can only be obtained by staying in their good graces.
As the old saying goes, "By gifts one makes slaves, and by whips one makes dogs."
Cultural: Getting in on the ground floor, and coming to dominate education, entertainment and/or religion. Ideally, overlaping, coordinated projects that might seem unrelated but subtley reinforce support for whatever ideology puts people in the pocket, makes them want to be there, but it's something that would have to have been simmering for a generation or two without some plot device. Mix in (manufactured) trends and fads? Text 382991 to decide who makes it to next season!
Combine all three, and you've got both the the physical tools for domination as well as the means to instill the fanatical loyalty. No single element would be enough to guarantee success, but if all 3 are addressed, you've got the potential for a global movement, or at least domination of enough countries to have the military means and will to conquer the rest.