How did feudalism in Europe end?

There is no agreed definition of feudalism, so one has to be careful how one answers this question. If you mean When did serfdom end? the answer is that it varied from country to country. On the whole it ended (in practice) in England in the late Middle Ages and had gone by reign of Elizabeth I.

In Eastern Europe serfdom was introduced in the late Middle Ages, at the very time when it was falling into disuse in Western Europe. In Prussia the serfs were emancipated in 1811, in the Habsburg territories in 1848 and Russia did not abolish serfdom till 1861.