I've found that I generally have to explain that, generally speaking, our Democrats are moderate right as opposed to far left (even the few genuine leftists among them are still close to center) while Republicans lean far right, at least in their rhetoric. Though rhetoric and posturing aside, they all
tend to be centrists in their actions no matter how contentious the issue may seem online.
The real power is in the corporations, though it's not a direct power. And even the ultra-rich have to watch their step when they either screw up badly (like the Gulf Oil spill in which too many demanded a scapegoat) or if they're dumb enough to mock the government during an election year (say
Martin Shkreli who would even impress Holland Manners with his audacity, and he ticked off the public with his openly contempt for both the public and the government--at the same time so many politicians were trying to impress voters and even the presidential candidates were warming up...had he said it at a different time he very well may have gotten away with it). What typically happens when executives are once again caught violating environmental and labor laws, or even ransacking the retirement investments of clients, is that they're fined a small percentage of the take and allowed to carry on, or at most fired with golden parachutes so they're not punished at all, just business as usual, but those not wealthy who got screwed over are out of luck.
Don't mention socialism in casual conversation. Many here can't tell the difference between that and communism, the latter evoking images of Stalin. Even plenty of Democrats steer clear of this.
Another example, the wealthy can build in dangerous areas that have to be regularly replaced (they do have to pay a little into some FEMA insurance program, but it would be the envy of anyone else) and get their mansions rebuilt at taxpayer expense which I don't recall Democrats decrying anymore than Republicans, but people with less money who lose their homes in a hurricane (who had to take what they could get unlike those who intentionally build their homes in dangerous areas) are out of luck who may find authorities indifferent to their plight, even if they have to fend off looters. Just one of the many examples of how Wall Street trumps Main Street, and why (through media owned by Wall Street) people can actually be happy to hear of every improving Dow and GNP even as inflation continues to negatively impact them (and buy financial advice that tells them to be sure to always sock away an amount into their savings when they don't even make that much to begin with).
Our FOX News has to be seen to be believed. Though I can relate to those who were unprepared for it. I first saw it at a fitness center and at first I thought I was watching a dry parody of right wing talk radio (it was actually Glenn Beck), and then realized this was the infamous FOX News (which I thought others had been exaggerating about, but nope, some of their reports are worthy of the Weekly World News). Heh, I mentioned a drinking game to play to it that could've gotten him killed (his parents kicked him out before he gave himself alcohol poisoning by taking a shot every time Bill O'Reilly referred to Obama snarkily as the Chosen One or whatever).
Those of you may find it surprising what we don't hear about. I understand the news of Obama's drone attacks were much more widely reported on outside the US, for example, while plenty of Americans were barely aware that such a program even existed (even FOX that was anti-Obama seemed to gloss this over, instead trying to portray him as spineless or even treasonous). Similar things could be said about Abu Ghraib, and most Americans simply didn't connect the sudden government hostility to the
ICC if I recall correctly (it was some world court that dealt with war crimes) to that and other incidents. And the details of it weren't as rubbed in our faces and quickly forgotten than in many other nations. Even when the news is about the same, the emphasis will change (the covers of TIME and Newsweek have been shown to have very different covers by nation, and while some is just plain marketing, US politics are often a big factor in how they're marketed in the US).
An Argentina friend of mine was confused by Americans not wanting a "national ID" (at least many years ago) when her national ID (yes, for Argentina, and she was well aware of the problems of her own nation) was a lot less intrusive and used than many of the forms of ID that we use.
Take everything you hear about what someone said, be it Obama or Trump, with a grain of salt as it's often taken out of context (or defended with mind boggling excuses). Even so, I got more than one email from someone in a foreign country asking me about if a politician really said something so outrageous or tried something and it was actually true.
But much more importantly, if you meet a citizen who happens to be registered with one or the other, don't assume they're like the obnoxious ones you can see all too easily on TV and online ('course if they're wearing or spotting a lot of political paraphernalia then it's a bad sign). Many are decent people who don't mindlessly march in step with the rhetoric of their party, and can cringe at the fanatics as well as having much more moderate views who can be quite critical of politicians of their party (not that they give other parties a break). And some are actually what are called "single issue voters" who primarily care only about one issue and typically side with the party they think is most likely to push that agenda in their favor, and so can be fanatics in that way but will otherwise surprise you, even seeming like they should be in the other party. In any case, many are individuals, not acting like body snatched pod people with an attitude, and actually care about America (and sometimes the rest of the world) more than they care about their own party (whereas others only care about their party and to hell with everyone else, including other Americans).
It's also worth noting that many here do not vote and are not registered with either party, or any party. I'm too lazy to look it up, but I think about half of eligible voters actually do during presidential elections (and probably as many are voting AGAINST the other more than for the one they're holding their nose to vote for) and even less than that in other elections. In many places it's taboo to bring up politics at all, and even people who are willing to discuss politics may have personal family rules of not discussing it while eating, for example. If you're a tourist with money it should be very easy to avoid any political discussions you don't want to have. You'd probably find our airport security extreme, but it's one all Americans have to face, not just you.
And all the "third parties" is even more "fun" to explain, as are the grassroots movements and citizen pushed initiatives.
This is all off the top of my head (and I know I left out some specific exceptions above). I could add a lot more (good gods I just realized how long this is!) and maybe I will later after I've had some time to mull it over on how I'd explain it to someone I just met (and whose country of origin I'm not sure of).