It seems surprisingly easy to create a small micronation today. Sealand, for instance, off the British coast, has hung around for decades despite an adversarial relationship with the larger government. Given the growing demands for more secrecy and less privacy, particularly on the internet, there has been discussion of making use of micronations to operate data havens on the high seas.
Let's consider, then, what options exist for getting your own micronation:
Coup: There's apparently one guy with an air rifle and some moltov cocktails that represents the entirety of Sealand's armed forces. Since he's seven miles out in high surf with moderate shipping traffic, a half-decent hunter could liberate the natives quite easily before they even realize that that schooner out there isn't a lost freighter. Sure, the inhabitants of sealand are technically British citizens, but it's your word against nobody's, if it's ever investigated. Still, it's diplomatically unpopular to take over a micronation so dramatically. Simply declaring ownership and arriving with the great advantage in numbers (say, three guys) would work just as well. Beware making enemies of the wealthy guy who may be to this day the Prince of Sealand.
Colonization: The number of abandoned oil wells and AA platforms is most likely rather large. The number of these that are in an appropriate range (outside of two miles, inside of the longest CAT5 cable you have) from land is probably smaller. Still, if you're looking for a good place to make your own, there's plenty of structures out there to consider. If instead you'd like some steady land beneath your feet, perhaps one of the many, many, many tiny islands out there suit you better. The problem with all of these, however, is that they aren't explicitly abandoned, and it may be that your new home is already owned. You may need more than an air rifle and moltovs to keep it.
Once you own your private nation, you need to set out to monetize it. I personally think your best bet is to use an array of direct wi-fi antennas with strong collector dishes to bring the internet out. This naturally implies that you have a set of receivers on the mainland, which would otherwise be your weak point. But by simply setting up as a TOR node and not using the connection for conventional traffic, you're good. Only encrypted packets are going in, and only encrypted packets are going out. Then get people to pay you to host TOR websites.