There is a lot of talk about the Fed printing money.
Is there any way to know how much new money is being printed and when?
The Fed doesn't exactly have a specific schedule when they decide to create a new dollar. Instead, they engage in open market operations, creating and destroying money as is necessary to preserve a certain interest rate for lending and borrowing. It's an ongoing process.
When the Fed meets periodically and they see that inflation is getting out of hand, they will raise that rate; when they see that the economy is weak, they will lower it. They change the target rate from time to time, but they seldom tell people exactly what they'll do in advance, aside from them recently saying that rates will remain incredibly low "for an extended period of time".
There are people who trade futures contracts based on what they think these rates will be, and the Fed does publish information on what the market thinks the probabilities are. That's probably the closest thing to telling you "how much and when".
If you want to know about the size of the money supply, ask the Federal Reserve; you probably want series H.6, Money Stock Measures. For an explanation of what the data series there means, ask Wikipedia: you're probably interested in M2, because that's what actually affects the economy, though M0 is closer to what they actually "print" (currency, bills and coins, and deposits at the central bank).
If you're concerned about the actual real value of your dollar dropping, the actual value drop is better understood by looking at either the inflation rate, or an exchange rate against a foreign currency (and depending on what you were hoping to use that dollar for, there are a couple of different inflation rates). The standard inflation rate which measures what happens in your day to day life is the consumer price index, published by the BLS. There are a variety of forecasts of this, but I'm not aware of any official government-agency forecasts.
The Federal Reserve is not the only way that money can be "printed." Every bank does fractional reserve banking, thereby increasing the money supply every time they make a new loan. There's a number called the reserve requirement which limits how much money each bank can create. Lowering the reserve requirement allows banks to create more money. Raising it will destroy money. But banks can also destroy money by calling in loans or being less willing to make new loans.
So when you look at the number of banks in the US, and the number of loans they all have, it's impossible to figure out exactly how much the money supply is expanding or contracting.
This chart summarizes the FED's balance sheet (things the FED has purchased - US treasuries, mortgage backed securities, etc.) nicely. It shows the massive level of "printing" the FED has done in the past two years. The FED "prints" new money to buy these assets.
As lucius has pointed out the fractional reserve banking process also expands the money supply. When the FED buys something from Bank A, then Bank A can take the money and start lending it out. This process continues as the recipients of the money deposit the newly printed money in other fractional reserve banks.
FYI....it took 95 years for the FED to print the first $900 billion. It took one year to print the next $900 billion.