What the Fed does to increase the supply of money is to buy bonds in the open market, thereby swapping cash for the bonds it buys. Normally the bonds the Fed buys are short-term government bonds. What has happened recently is that the Fed has dramatically increased its purchase of bonds, and it now owns longer-term Treasury bonds, mortgage backed securities, commercial paper, and a host of other esoteric debt securities. This graph graphically shows how the Fed has increased it's balance sheet over the past six months. So when you hear or read the terms "printing money", "monetary expansion", and "increasing the Fed's balance sheet" they all refer to the same thing.
These actions by the Fed are of extreme consequence, and I believe they dwarf the stimulus package in terms of potential effects on the economy, both in the short-term and long-term. There is really no doubt that these actions will cause inflation, which is what the Fed wants to do in the face of the deflationary risks caused by last year's financial crisis. The questions that we need to keep our eyes on are: What will be the longer term effects of these policies? Will we have long-term higher inflation or hyper-inflation? And will the Fed be able to change course at the right time and avoid causing an inflation crisis?