Well, being a fellow American and not knowing a lot about what exactly it is that the EU does, from what I've gathered, by being in the EU, the UK basically has trade deals with the entire EU. As article 50 is enacted, the UK will have to negotiate new trade deals, I assume with the EU representing all relevant countries, not each country separately.
So, as of now, no one knows what those trade deals will shape up to be. The UK could end up with much worse deals than it had before, and if this happens, it will drastically affect their economy.
However, I personally believe that this is all just an over-reaction, as I believe that Brexit will ultimately turn out to be the best decision they ever could have made. I don't know how old you are, but the market is always very reactive, over reactive, in fact. People tend to panic at any sign of instability and hastily liquidate their assets.
I also believe that there are also some shenanigans going on, with globalists manipulating prices to try and dole out some kind of punishment.
As for what is being reported and how, of course you would expect the liberal media to try and declare it a disaster.
Another aspect is that with the UK leaving the EU, this is likely to open up a whole can of worms with other countries conservative parties following suit. And if there is any reason for investors/speculators to be afraid, this is what they are really scared of. A complete collapse of the EU would mean that they would have to completely rework their portfolios.
But again, that doesn't mean that it is bad. They will just have to invest in different things now, and the market will recover, as it always does. Until of course, the day comes that it doesn't. And that will be the happening of happenings, and a day we should all be looking forward to.