How did the vikings control england?
They didn’t do squat. They barely touched on England; it was mostly Scottish and Irish monasteries that were the goals of their attacks. They never controlled anything but their own land in Scandinavia. The Vikings looked for easy pickings, and because England was pretty good at defending themselves, they didn’t think much of raiding it, let alone controlling it.
The answers given so far are frankly rather poor. The Vikings ruled a large part of England for many years, the area was called the Danelaw. It’s why many people from eastern England, from Yorkshire down to Norfolk are tall and blond haired, they have Nordic ancestry. The Danes were very fond of appointing puppet rulers. They could usually find some thegn from a Saxon kingdom willing to take orders from them in exchange for getting to sit on a throne.
