Basic things to know to understand this: I am using a general knowledge here, not necessarily in depth, and basic definitions.
Conservatives are people who like the status quo. They generally like things as they are, or want to go back to a "simpler, better"time. They generally, in the U.S., argue for' smaller government ' but not of it will effect military, businesses, etc. Notice I said "generally"; some will have different views.
Liberals are people who want to expand liberty, and generally see government action as the way to do it. They want everyone to have what they need, and seek laws to make that possible. Again, I said "generally".
Fascists believe in absolute governmental authority, in conjunction with business.
Socialists believe the means of production should be in the hands of all the producers. This means anyone involved in making a product should share equally in the profits. It's actually a economic theory, but is used in politics to stand against...
Capitalist, who believe in the market, as in, if it makes money, it's good. If it losers money, it fails. This, also, is an economic theory used in politics.
Progressives are liberals in steroids. They generally believe that government should take the side of all the people, but especially the economically and socially marginalized members, over virtually everything, especially Big Business.
Libertarians are... Well, it matters which ones you mean. But by definition, they seek more liberty for all and can be summed up in the adage "your rights stop where mine start". In other words, what you do with you and yours is your business, until you interfere with what I do with mine.
Anarchists... Well, again, we have that "there's alot of different types" issue. But most anarchists can agree on these basic ideas:
Government corrupts. It continuously seeks to limit liberty "for the greater good", which cannot be the greatest good if it limits liberty. Liberty, and the freedom it brings, ARE the very definition of greatest good.
A word about corruption. We generally think of it as bribes, taking money or kickbacks. But it comes in many forms. Taking a side against or for something, which is good for you and yours, but screws someone else, is corrupt. "By any means necessary" is corrupt. "Might makes right" is corrupt. Anything--ANYTHING--that takes away of limits another person's freedom to give you advantages, is corrupt.
I've passed over alot and ignored and/or simplified much. But like I said, this I'd the simple version. More in depth to come.