How did Karl Marx become famous?

Karl Marx became famous when a work he wrote with his friend Friedrich Engels called the "The Communist Manifesto" was published in 1848. The pamphlet, commissioned in 1847 by the newly created Communist League of London, laid out the principles of communism. It was both short and stirring, and it ended with a call to action, calling on the workers of the world to unite, rise up, and throw off their chains of oppression.
As is often the case with works that catapult their authors to fame, "The Communist Manifesto" appeared at just the right moment. The year 1848 is famous for the revolts and revolutionary furor that broke out across Europe, most notably in Prussia and France. Both those countries had forced Marx to leave because he was too radical. His manifesto appeared at a time when people were hungry (usually literally as well metaphorically) for lasting changes to political and economic systems that seemed to grind down too many people for the benefit of too few.