This is called dynamic positioning. Drillships are very expensive to operate but can drill in any water depth. To connect the drillship or semisubmersible to the well on the bottom of the ocean, a marine riser, a flexible, metal tube is used. The drillstring runs down the center of the marine riser. The marine riser gives a closed system to circulate drilling mud just as on land.
Offshore wells are very expensive.
It costs about 5 times more to drill the same well to the same depth offshore than it does on land. If you are having problems printing this article, click on a portion of the text of the document.