Hmm...I can undoubtedly quote wikipedia or some other sources on what the terms REALLY mean, but you can obviously do so as well. So with the risk of being totally off (I really hope not
) , I'll go from the top of my head...
In any case, I'm presenting the main view behind the ideology. I'm unsure to what degree countries truly were ever able to implement these (assuming they wanted to in the first place), so it might sound a bit caricatural.
Communism is where the country owns everything. You can't have personal possessions other than what's been granted to you by the state. At least in theory, said state treats everyone as equals and distributes wealth among its citizens, regardless of their worth. While this effectively prevents the rich from getting a stranglehold upon the rest of society, it also removes any motivation people have to excel at anything.
Capitalism is the direct opposite: the individual owns everything and the government is practically non-existent. Taxes are low and only really serve for the most basic of basics. As such, talented individuals have the most to gain by working hard. The main problem with it is that it's like playing a sports match where the referee's vote is worth less than the player's. In other words: companies can grow to such sizes that they effectively hinder competition to grow to the levels they've grown to.
Socialism is somewhere in the middle ground between the two. It has a strong government, but one that is in service to the general public. Services that are deemed a necessity are facilitated or sponsored by the government (medics, schools, ...) but only partially owned by them. They also meddle in the business world in the sense that the benefit of the many outweigh those of the few. In other words: environmental restrictions, anti-monopoly laws, ethical laws and things like that. The main problem would be that it's hard to define. Is internet deemed a necessity in today's world, or is it a luxury? If culture and religion should be preserved, should that also go for the Flying Spaghetti monster? And so on...
My vision is most likely blurred by my own preference (the latter). Nevertheless, I feel that this gives at least a broad overview of the differences between 'em.