Nothing - absolutely nothing frustrates me more than when someone puts Nazism in the same sentence with Communism and Socialism, like they're interchangeable terms or synonyms or something. They are not. They just aren't. And you're a frakin' idiot if you continue to insist they are. There's no nicer way to put that - you're a goddamn fool.
But - Post-Modern Enlightenment supports learning. If you honestly did not know the difference, that's something totally different. While there are dozens of resources out there to help you tell the difference, here's a quick primer:
Fascism - Fascism is probably the most diverse of the three ideologies. However, all the strains of Fascism have several things in common: Extreme nationalism, State-regulated Capitalism, Extreme-xenophobia and xenophobia related tendencies (for instance, the belief that one race is superior to another), State/hero worship, and a strong Patriarchal tend (calling it the "Fatherland", for instance.) Fascism is very masculine and full of machismo, pumped to the brim with testosterone. Fascism can combine with religion to form Theocratic Fascism; fascism usually ends up combining with religion in some ways anyway. Fascism is a Right Wing Ideology. It claims to be middle of the road but it's not. While some elements are lifted from the left, fascism itself lies strictly on the right side of the political spectrum, regardless what liars like Rush Limbaugh, Glenn Beck, and Bill O'Reilly say.
Nazism - A specific form of fascism. Nazism comes from Nazi, which is an acronym for "National Socialist's Party", in German. It has all of the features of fascism, and featured some minor elements of socialism to help with the economy. Contrary to popular belief, Nazism was not responsible for pulling Germany out of the depression - it was a war economy that did that, and any four year old could run a war economy. Nazism is a loaded term anymore; to play the "Nazi" or "Hitler" card on an argument - any argument at all - garners shouts of "Godwin!" from others, because you just invoked Godwin's Law. No, the Nazis were not gay. No they were not leftists. Yes, they did persecute and execute Christians. In addition to gays, Jews, Roma, Mentally and Physically Handicapped, Labor Unionists, Communists, Socialists, and any other "undesirables" in the new vision of Fascist Germany. That I even have to bold this and put it in red is a damn shame.
Communism - Communism is easily defined. It's a revolutionary ideology, that posits that throughout history the poor have been held down by the middle class, who do so to receive scraps from their masters, the wealthy. The idea is that the poor should revolt and overthrow the wealthy and the middle class, dissolving all property and dismantling, eventually, the government itself into a start of anarchic commune existence (community and communism share the same root etymology). There are several different "schools" of communism, but the one most Americans are familiar with is Stalinism, or Red Fascism, which is what you'd get if you combined the revolutionary nature of communism with the other features of fascism.
Socialism - Socialism is a strict economic philosophy. Where the other two are social and economic philosophies, socialism is not. At it's heart socialism is just the admixture of government and private enterprise in the government to varying degrees of each. That's all socialism is - just government and private enterprise sharing the market. The government usually regulates private enterprise to make sure that private enterprise doesn't exploit people, and the government takes responsibility for different tasks that private enterprise either can't afford to do or won't do (recycling and flood insurance, for instance). America is a socialist country and has been for the last 100 or so years. Because it's a economic philosophy and not a social one, socialism can combine with any form of government; from democracy to democratic republic to fascism, to theocratic fascism. Socialism and "society" share the same root etymology.