Specifically, the government was supposed to be a temporary crutch to aid in the transition from a traditional bourgeoisie/prolateriat system into true communism. But that put an awful lot of trust in just a few people, and somehow, the temporary crutch lasted about 80 years in Russia, the first nation to go communist. The system was supposed to be a retort to capitalism, which Marx saw as the rich getting richer and the poor getting poorer. But the "interim" government in Russia/USSR wasn't much of an improvement on that. The masses were still poor.
Of course, the fact that the Communist Manifesto was intended to be applied in an industrial economy, such as Marx's home country of Germany, and Russia was an agricultrual economy, didn't help matters much.
The reason why Communism is still around in China is because the Chinese government has made a lot of concessions to capitalism. Similarly, the US has made a lot of concessions to socialism (which is what the USSR system actually was... fascism and Naziism were the same way) in the way it operates.
In true Communism, everyone owns an equal part of everything, and everyone shares according to need. In true capitalism, the market decides and the strongest survives, much like Darwin's theory of natural selection. The only problem is that both ways' ideals count on humans being basically good. Many are, but it only takes a little bit of greedy scum to ruin the whole thing.
If we had a true capitalist system, there would be no government regulation of business practices. If the working conditions were atrocious, the worker would have to grin and bear it or find a job elsewhere. If one company was able to force all its competitiors out of business, then tough shit. There would be no antitrust suits against Microsoft, for example. Under true Capitalism, Netscape shouldn't have stayed stuck on 4.7 for so long; it's not Microsoft's problem that they released two or three new versions of their IE software in the time between Netscape 4.7 and Netscape 5 (which was so long in coming that they just skipped 5 and called it Netscape 6).
So that's a basic rundown of capitalism and communism.
