You miss several links that are essential to maintaining monetary
balance,
Zen baby. Banks give money to companies and consumers....but the reverese is also true. Most of the money banks give out for loans are from
deposits made by people or organizations. With enough
capitol, which most banks have, they can lend out huge amounts of money, only borrowing from the Fed when they are near the
reserve ratio which is the minimum amount of their money they have to keep onhand incase there is a mass withdrawal a la the Great Depression.
The Fed also spreads money through buying or selling of stocks (the first to increase the supply of $ the second to lessen the supply). Also I don't know where you got the idea that the Fed is trying to get more money that they put out. They attempt to maintain economic balance, sometimes increasing the money supply to spur growth, other times lessening to retard inflation.
I think your confusion rests on two main points. First, money has no inherant value. It is only worth as much as we, or more accurately the economy, decide it is. The Fed simply makes this money. The more of it there is, the less its worth if the economy remains stable. This is the nature of currency; gold has no real use but was for a long time the basis of trading.
Second, as I said, money for loans can usually be traced to deposits rather than Fed loans. The moneyis basically recycled over and over, thus creating an illusion of more than actually exists. A dollar can simultaneously be in a bank account, loaned to a company and a check to an employee.