There are some minor to mildly significant spoilers for the Force Awakens here. While most of this deals with what precedes the events in the film and things that aren't handled during it, if you want to be completely spoiler free, maybe come back after you've seen it.
While I very much did enjoy Star Wars: The Force Awakens, there is one thing that was distinctly absent from the movies that has irked me and a couple of other fans. The question of the state of the Galaxy is largely untouched in the movie. Perhaps this is for the better, and thanks to the negative reaction to trade negotiations in the prequels, but The Force Awakens' focus is almost entirely on the characters and their own personal adventure.
This leaves a quite a few gaping questions within the lore of Star Wars that are largely untouched, leaving those who even have a glancing interest in what is going on in the Galaxy a little perplexed. Who are the First Order and where did they come from? Why is no political power opposing a group that have appropriated the iconography of a previously overthrown dictatorship (that even uses Stormtroopers!)? What happened to the Rebellion after the Galactic Wars? There is just a lot of questions that The Force Awakens doesn't even touch.
Well, I've done a little digging and thought I'd try and bring you a shorthand guide of what I could find. Using new canon title like Star Wars: Aftermath and Star Wars: Shattered Empire on top of fan discussion, I think I have formed at least a decent picture of what is going on. Do note that not all of this is confirmed, has some fan made logical jumps and could change in the future to serve to movies or the expanded universe. This is just my own understanding of climate based on the information I've been able to find, with a smattering of my own interpretations. The fact of the matter is, there isn't a lot out there on this, so we're dealing with what little we have. Do feel free to correct me if you think I am off base anywhere.
Without further ado, let's get to it:
So, who is the ruling power in the Galaxy?
This is something that got lost in the movie for me, and was one of the key things to understanding the political situation in a post-Empire world. I thought it was a bit strange the galaxy seemed to have no problem letting a very clear Empire like party take over the galaxy a mere 30 years after the fall of of the regime. The answer is that The First Order aren't the ruling super power. The Republic is.
What is the Republic?
As previously stated, The Republic are the dominant superpower in the Star Wars universe right now. The Republic were the democratic power in charge during the prequels, before getting overthrown by the Empire. The 'New' Republic has grown out of the Rebellion's victory against the Empire in Episode VI, and has remained in power in the ensuing years.
Who are the First Order? Why do they have Storm Troopers?
So, The First Order. After the defeat in the Return of the Jedi, there were still many who were loyal to the Empire who scattered. There was a bunch of in-fighting by high ranking officials to take control of what remained…but, long story short, this all culminated into a big battle on Jakku where the Rebellion finally stamped out what remained of the Empire (and why you see Star Destroyers crashed on the planet in the beginning of the Force Awakens.)
After this, there were some who believed that the Empire would rise again, but it would need to rebuild in secret. This is a bit confusing, since there are a few factions thought to be toiling away in the dark, but clearly the only one to get its act together thus far really is The First Order (The Knights of Ren in toe). They worked away in the shadows for decades, and have worked with the Sith to regain their power.
Simply put, they are a group that grew out of old members and supporters of the Empire who seem to be working actively alongside Sith.
So who is Supreme Leader Snoke, and why does he want to re-establish the Empire?
You might consider this entry a little more Spoiler-y than the others.
Snoke is the very top of the First Order. We can assume he is a Sith, having taken Kylo Ren as his apprentice, while putting General Hux in charge of running the military operations of the First Order.
Besides that though, Snoke is more or less a complete unknown with very little about his motivation or intentions made clear. You'd assume it would be 'to get to power', but it's not clear why he would side with the The First Order, or perhaps even create it. We also don't know how he became a Sith (which we are assuming he is) and if he had any relationship with Palpatine or is self-taught in the ways.
Updated: I was aware of this interview with Empire, but forgot to include it in the final write up. J.J. Abrams said that Kylo Ren isn't a part of the Sith, but did say Snoke was part of the Dark side. On Kylo Ren, Abrams said, "He works under Supreme Leader Snoke, who is a powerful figure on the Dark Side of the Force." Whether that means he is a Sith or not, we don't know.
I think this quote from Abrams gives a very interesting perspective on understanding where the First Order came from:
That all came out of conversations about what would have happened if the Nazis all went to Argentina but then started working together again? What could be born of that? Could The First Order exist as a group that actually admired The Empire? Could the work of The Empire be seen as unfulfilled? And could Vader be a martyr? Could there be a need to see through what didn't get done?
This does leave the question of where the Sith are and what their current status is. If there are Jedi, there must be Sith, as is the balance of the Force.
Why aren't the Republic worried about The First Order?
As best as I can tell, The Republic are indeed aware of The First Order. After the war, they massively de-militarised, dismantling a large portion of its armies. Now run by the Chancellor Lanever Villecham, his focus is almost squarely on trade relations, and doesn't seem that fussed about war as a result.
While he recognises The First Order, he doesn't see them as a major threat and won't get involved as long as they follow the boundaries of the Galactic Concordance, a treaty signed after the fall of the Empire.
Shouldn't The New Republic be worried about the Starkiller weapon?
You'd think and you'd have assumed someone would have noticed the massive amount of resources flowing towards one part of the galaxy or, you know, an entire planet, but we'll just assume that is a lore oversight unless we are told otherwise.
Who are the Resistance?
So, now we get to the Resistance, the group that 'the goodies' fight for in The Force Awakens. They are somewhat of a splinter of the New Republic headed by Leia Organa. They have broken away from the New Republic (who seem fine with that as they see Leia as a little crazy).
As The New Republic didn't seem all that fussed by the rather troubling emergence of the First Order, the group splinted off and have taken it upon themselves to keep the First Order in check. They've been fighting a quiet war with the First Order for some time, being a thorn in the Imperial's side for years.
Are the Republic helping the Resistance?
This is a little grey and not necessarily defined as best as I can tell. The First Order certainly think so, but it doesn't seem the New Republic sanction these attacks by the Resistance.
Does Luke Skywalker fit into this at all?
Not immediately clear. He certainly tried to form a new Jedi Order in the new continuity, much like in the now scrapped expanded universe, but to what success isn't clear. What seems pretty evident though is that this Jedi Order isn't around during The Force Awakens, at least in a political sense, so the Jedi don't seem to have a stance just yet.
As for Luke personally, we really don't know. He certainly has personal stakes in the people involved in the war, but he has not been physically involved, that is for sure. Whether he has been using to Force to help, or is even aware of what is going on won't be known until the future.
And that just about covers it I think. If you have any other questions, I'll see if I can find any answers. Hopefully you at least have an understanding of what is going on in the political landscape around The Force Awakens now, even if the movie didn't tell you.