How does the dollar increasing in value cause our the DOW to drop ?
Supply and Demand. The more dollars there are in existence means it takes more of them to buy anything - oil, gold, cotton or stocks. Conversely the opposite is true.
At a certain level a cheaper dollar makes our exports less expensive which gives a boost to the stocks of companies in this niche. But this doesn't explain why the entire market is now almost completely correlated as one.
What does effect the market is that a weak currency makes for a perfect vehicle for a "carry trade". This is where you borrow in a cheap currency at low interest rates and buy items you think will go up in value faster than what you expect the denominated currency to appreciate. This borrowed money finds itself being rolled into the stock market as well as other speculative venues. For the past couple of decades the Japanese Yen has filled this roll (and see how well that's done for their economy). Now it seems that the US$ is the currency of choice.
The average American looks at the morning paper and sees that the DOW is up and thinks, "Oh, the economy is getting better." This is not true and might even be a counter-indication of the counrty's health.
But the Fed is convinced that stock appreciation will inject confidence into the American public so they are driving the stock market up. However their actions in doing this lead to a weakening dollar. With the end of QE2 next month the dollar should strengthen because there will be sudden decrease in supply. This should cause every commodity to go down in price including the stock market. The market makers at this point are trying to divine what the Fed's next action will be when there is a dramatic drop in the markets and most are guessing that they will respond by ramping up the printing presses once again. That is the reason that horribly bad news like yesterday causes the market to go up while good news has the opposite effect.
It is because of this that the market is now disconnected from reality. Only those who are inside to what the Fed is thinking can win while the rest are merely lucky if they guess right.
Sorry, this is a long answer to a simple question and doesn't even cover all the points - but it's a start.
JTS