Well that is a significant piece of information, don't you think? Especially since it countermands your previous statement that the world had only half a billion people.... I suspect you've got an alien invasion of Earth in mind, don't you? You're writing a movie or a book, eh? Well once you've written it, maybe you could share with us the bits of glory in it relevant to all this nice information that has been provided, please? We like reading.
My own take on this is that you've already been given all the most pertainent suggestions, you simply need to put those pieces in place.
Most of the time, when you want some one to do what you want, you have to use a carrot-and-stick approach. Probably the best thing to do first is reveal the carrot. "We need this unobtrusive island over here, and in exchange, we're willing to give you the secret of fusion reactors."
Most governments would grab that right up. The populace's reaction will depend on their country. Restrictive governments will probably not tell their people anything, or only what they need to know. The rest of the world will almost certainly, at some point, detect the aliens, and want to know what's going on. governments may try to keep the secret from the populace, in order to also benefit from what can be gained, but they may also release the details to the public, in order to gain the power of popular opinion.
"The Chinese have aliens helping them, we need to take them down before they decide to conquer the world." What happens when the whole world gangs up on that nation that helped the aliens?
Nothing... the THREAT of violence is the key here. This is also the Stick part of the deal. Once all these crazies start thinking they need to invade China to get the aliens to share their nifty tech with the rest of the world, then if the aliens wish to protect their base, they are going to have to threaten to use force, and a suitable demonstration will have to be arranged. Note that you should never threaten something you are unwilling to carry out; on the other hand, that doesn't mean you can't make yourselves look tougher than you are.
A lot of the people of Earth are "free". That means the gov't has to con them into doing what they want them to, instead of just ordering it and expecting the threat of all those soldiers on the street corner, or the MIBs, coming to get them if they disobey. The aliens don't necessarily want to start a war here, so instead of blasting apart some of the critical infrastructure (including communication satellites), they hijack what they can.
You take over the satellites, you can squelch the various gov'ts from preaching to the people, AND you get to preach your own message. If there is some centralized something or other (like a giant power station to power the planet, or a few sources of water, or the air recyclers in a vacuum world) then you can also take these critical things and threaten to destroy them if the people don't settle down. As long as the aliens don't play the part of reptilians from Sirius, trying to strip our planet bare of all its resources and people, the world might be willing to settle down.
One potential thumbscrew you can tighten, if the world is human or human-like, is to threaten their ability to reproduce. For instance, say you are able to tailor a virus that shuts down the reproductive system of the dominant lifeforms (the humans). Now life is a rather precious commodity (again). You don't go throwing it away on pointless raids that succeed only in getting your people killed, cuz there WON'T be replacements. Then you say "Play nice and we'll let you go back to normal. We just want this little base over here, and we even paid for it. Stop making us hurt you. You keep pissing us off and we'll glass your asses."
So basically, you took from them what they wanted (normality), and then you offered it back to them, if they'd stop being so senseless and just let you live in peace.
Of course, there are places where you just CAN'T force people to do what you want. You can try assassinations against the leaders who are stirring things up, you can try demonstrating your power now and then, and you can try public relations. It's hard to judge what's likely to happen, but in a human society, you're going to have some people go along with it, some people try to take advantage of it, and some people oppose it. If you try to put the best face on it possible, play by their rules, and establish yourself as friendly, you should be able to carry it off. If you go and force your way in, beat down resistance, and act like your goal is to take over the world, then you'll have problems.
People fight hardest when they feel they have nothing left to lose. As long as you never make them feel like that, you have a chance of getting them to do what you want. People also don't like having their world turned upside down. If you try to minimize your effects on their lives (even the gift of fusion would cause riots as oil barons stirred up trouble about all the evils of free, limitless energy), they will be more inclined to ignore you. Failing that, take their normality away, and then offer it back to them, so that they can see what the alternative is.
When all else fails, glass them, and use them as an example to the next world (if the carrots don't work).