The United States has embraced socialism from the very founding of the nation. The Constitution nationalized the carrying of mail when it created the post office. Mail delivery is a service that was previously done by private companies, but the Founders recognized the importance of a reliable and nationwide postal service.
Public ownership of the commanding heights of the economy.
Libertarian <-> Authoritarian
This is exactly how my uncle thinks. Except if the government does a whole lot of stuff, like lots and lots, but is led by a Republican, then it is a God supported Republic and bastion of Freedom! 
My brother is to my left a bit. My sister is pretty far to my right. The two of them are often not talking due to their political differences. The last time I was with them, they were arguing. My sister, wanting to insult my brother, called him a Socialist. My brother replied that he was actually closer to being a Marxist. I just ignored both of them.
I think at the bare minimum it is the acceptance of the fact that some people are able to live very well at minimal effort, and some people are forced to struggle to survive. And a desire to rectify that, usually through government action in a democracy but not always. All sorts of solutions to that problem have been tried with different degrees of success (or failure, if you prefer), for the entirety of human existence.
And the ever-wise Kenobi kills the whole thread in the first sentence of the first reply. Bravo Good Sir.
With a secondary shout-out to @Sam_Stone for his well-chosen taxonomy of legitimate -isms and his conclusion that it’s (substantially) all just name-calling now.
It’s sad that I had to look Richard Wolf up on wikipedia to determine whether he was a liberal mocking the conservative thought or a conservative expressing it.
In the US culture wars Socialism is the new Communism.
In Europe socialism is a very nuanced concept. Lots of different interpretations that build on communitarian cultural tradtions. A couple of world wars really rammed home the idea that people have to stick together and the state has an important role in that. Not so much that they breath down your neck with rules, but should be there to take care of the fundamental services people need in a modern economy. Health, education, social welfare, police, military, fire service. Market economies are not good at these sort of public services that everyone needs. Some interpret socialism as the state controlling all of the economy. That is not socialism, it is communism and in the places it has been tried from time to time, it has been found wanting.
Drawing the line between what should be delivered by competitive markets and what should be delivered by the state financed out of taxation. That is the challenge. There is no ‘one size fits all’ answer and it requires a mature and informed conversation and political debate rather than a lot of simplistic name calling. Half the political parties in Europe seem to have Social in the name. A fair number also have Christian as well, which give the clue that they are informed by something quite different from the ideas of Karl Marx. Some of the most successful private companies had strong communitarian values and ran all kinds of services for their workers before they were later provided by the state. The social element is informed by several, quite different examples of people working together. Local governments, religious institutions, charities, labour unions and enlighten companies. They arise from a common need to deal with the fundamentals of living in a modern economy and the recognition that the state has the economies of scale to provide important public services effectively. The political question of where you should draw the line about what the state should do and what should be left to markets is still a bone of contention that gets chewed on from time to time with yahoo’s on both sides.
There is a definition of a normal country as one where the political conversation spends a most of its time arguing about healthcare and education.
All of these definitions are born of social consensus and shift meaning over time, but I’d say that the clearest and most useful definition of socialism is something like: Collective control of productive forces. That’s narrow enough to exclude regulations and other market interventions, but broad enough to include pre-Marxist and Marxist traditions.
I think a lot of the confusion on this issue comes from the deeply ideological assumption that capitalist social arrangements represent the natural, default state of society. If you were to take a long journey through human history and civilizations, you’d be hard pressed to find a society in which markets produce large capital surpluses which are then reinvested until you reached Europe in the Pre-Modern era. That arrangement is one that was deliberately constructed and is maintained on an ongoing basis by state action. You only need to took to real estate to see it in action. We’ve all heard that 1491 Native Americans didn’t have a concept of land ownership (which is an over-generalization, but it was true in some societies), but the medieval Normans didn’t have our concept of land ownership either. The idea that land can be freely alienated and traded would be perplexing to a feudal society. It’s only through hundreds of acts of state-endorsed recordkeeping, of court cases, police-backed evictions, etc. every day that the land market is maintained. Without all of that state intervention, we’d default to something messier. It’s not natural; it’s as artificial as socialism.
Class
Socialism is: transformation into a classless society.
Of course there is a huge difference in the how and when between the revolutionary communist and the parliamentary social democrat.
In general, I would personally say that the word “socialism” has been used by so many people in so many mutually incompatible ways that it’s effectively meaningless. Beyond that, it’s been actively advertised as the definition of evil by a large enough group, sufficiently effectively, that you’re just screwing yourself over by trying to use the term for anything that you think is a good idea.
Realistically, socialism is a term that meant something at the beginning of the 20th century. In the 21st century, I would only recommend using it when you’re discussing pre-1960s movements. There’s been too much history between the original release of the concept and how all of the sub-movements have evolved since then - including hippy groups, neo-fascists, communists, anarchists, and right-wing religious groups.
Ditto for fascism. If you’re using it to describe anyone who isn’t Hitler, Mussolini, or someone else from that era then - most likely - you’re not going to be using it correctly and there’s really no upside in linking your movement to the term.
ETA:
This is my understanding of what the term originally meant. Marx thought that it required levelling the field, through force. In the US, we already had a meritocracy going by the time Socialist rhetoric made it over, so the movement never gained much foundation here. It was more popular in places with official over- and under-classes like Russia, which still had a functioning imperial system.