So has anything been done since the initial Brexit vote? Like, at all?
Yes. Article 50 was triggered. This is the formal declaration of leaving (and has a time limit, since extended a few times and a further one is a hot topic right now but tricky for a whole bunch of reasons on both the EU and UK side of things*) as the vote was essentially an internal matter, technically not legally binding either -- direct democracy is not a major feature of UK politics, certainly not a common one (if you are more familiar with the US style of things where everybody down to fire commissioners are voted upon as are individual bills then such a notion is alien to most UK peeps), but ignoring it entirely is rather hard to justify.
However said triggering happened seemingly without much of a plan on what was going to be asked for (the original referendum had no particular choices here, and little in the way of "we will be doing this if you vote this") and wide division across all the various concerns. Said concerns, though there is obviously overlap and pragmatism that blur things, fall into four main camps which are roughly
The essentially hard exit to become just another country in the world, though presumably some negotiations done in short order as geographical location, historical and cultural ties and richness mean it is worth it. I don't know if this has been legally ruled out at this point but to attempt it would be a legal minefield, though the EU could also turn around and say you are done and have it happen by default as it were.
The so called softer approach where the seat at the table is lost but some of the rulings still apply so as to facilitate trade more easily. Harder to sell to some people as Brussels is used much the same as Washington/DC is used when people talk about federal rulings in the US, and much of the campaigning was about taking back power. However also not a position without its supporters among those that voted to leave.
While the opposition side has recently been seen to somewhat coalesce around the the "stop it if we can" types (though still not enough of a majority to do anything real**) then there was the "it is a bad move but if the people want it then make sure it is a good deal".
None of said camps are anything close to dominant over the process as a whole and while party lines are a reasonable predictor there are some very notable exceptions in all of it -- the conservatives (the people that promised and held the vote in the first place, that lost a lot of support but still just about retained power in the subsequent election, albeit by teaming up with a local interest party in Northern Ireland) have some major dissenters here (some left, some were kicked out of the party, and today they are very much in a minority in government and have taken an absolute hammering at various other levels) there are others on the other sides that vote differently (sometimes pragmatism, sometimes their assessment of the thing, sometimes because that is what their constituents voted for in the original referendum).
Internally in the UK as a lot of this is uncharted territory, and the UK does not have something like a codified constitution as much as lots of doctrine on the matter, then there has been a fair bit that has been figured out about what goes in such scenarios, and internal UK laws passed about what needs to happen (one of the main ones being that the UK parliament gets to approve the deal first, and seemingly another saying that leaving without a deal is not an option).
A few quirks have been cleared up (the territory of Gibralta borders Spain for instance) and while the main negotiations have somewhat stalled there was the agreement the EU and negotiators (despite various flavours of incompetence, being without direction, being hamstrung and various resignations, firings and prime ministers/major ministers going themselves instead) came to concerning what to do in the meantime while the main negotiations could be continued (the so called backstop agreement) but that was rejected so harshly (on essentially multiple occasions, which itself is rare as returning things multiple times is not the done thing) that said series of rejections is now going to be a major historical note in UK politics. That said present UK politics is something of a series of major historical notes so that might end up being drowned out somewhat.
Outside the EU there have been some overtures made to various countries as far as increased trade relations but most of those are waiting to see what will happen with leaving the EU lark first, the US among the more vocal for the harder exits (at least this presidency, the previous one differed a bit) where others do other things (For instance Canada, which has its own historical and current political ties with the UK, at this time being in the process of creating greater ties with the EU, indeed it forming one of the major models people looked at when considering what position to take).
*the UK side of things is probably obvious here but EU wise their next major budget plans for the next however many years are set to begin (this being one of the major functions of the EU) and if the UK is still involved then that makes things a bit tricky -- the UK being both a source of revenue and a cost centre within it (in simple terms on a balance book the UK is a net profit for the EU but you still have to allocate spending and predict income), to say nothing of having a leaving party in a vote on direction, as well as their own vested interests, being a less than desirable thing to have.
**the calls for an election came thick and fast for months, however during this proroguing lark the notion was floated and rejected as "not enough time" or something. If they thought they had a chance to enact their will then do you think they would have blocked an election?
So yeah cynicism is quite justifiable, and the notion that the UK is some kind of old hand punching above their weight at international politics has taken a major kicking, and a lot more things should have happened but to say nothing happened is also not correct.
The british side later brought in a formal complaint - that a press conference indoors was promised - and the promise not abided by.
