An offshore oil rig is, generally speaking, a floating electric drill. It consists of a building on top, a large pipe that sticks out the bottom and into the ocean, and a BIG drill at the bottom of that pipe to cut through the bedrock and into the oil fields. There are five basic types of oil rigs:
1) Fixed Platform
A fixed platform is the sturdiest, most permanent type of oil platform. It is a building in water, complete with foundations in the ocean floor, reinforced concrete legs rising up to the water's surface, and crew quarters in the building set on top of the rig. Normally the fixed platform is built on land, assembled at sea, and then floated to its final destination, where it is sunk into the ocean. It can be used in waters of up to 520 meters deep.
2) Compliant Tower
The Compliant Tower is the skyscraper of fixed platforms, usable in waters from 460 to 910 meters deep. Its construction resembles that of a skyscraper, too. Its supporting legs, though permanently drilled into the ocean floor, are not rigid as in the case of a small fixed platform. Instead, to handle the massively increased stress and strain, they are built to be somewhat pliable.
3) Semi-submersible Platform
The iconic image of an oil rig is the semi-submersible platform. It is basically a floating hotel, with a big drill underneath. It can be used in water of any depth, and is connected to the ocean floor by chains, rather than a permanent foundation. It can be raised or lowered in the water by adjusting the amount of air in large on-board ballast tanks.
4) Jack-Up Platform
The jack-up platform is intended for relatively shallow waters, roughly 170 meters at the most. It is a midway point between the fixed platform and the semi-submersible platform, in that it has rigid legs, but that these can be collapsed under it like a folding chair when time comes for it to find a new home. Once it has moved, the legs are unfolded, and the structure is "jacked up" out of the water, much as one would jack up a car.
No oil platform can compare to the drillship, at least not for the depths to which it can drill. The drillship can drill more than two miles deep, and it relies on GPS to maintain position over the well. It is used mostly for exploratory drilling.