When the Fed buys things it either prints currency or writes checks on itself. Commercial banks can use either currency or checking account balances at the Fed as reserves against the deposits their customers have. Banks trade reserves over night. The interest rate on these loans is called the Federal Funds Rate. The Fed targets this rate when conducting monetary policy.
Here is information on the Federal Funds Rate:
On the free market, the fundamental interest rate is determined by people’s time preference, i.e., their preference for sooner satisfaction instead of the same satisfaction later. Because of this preference, present money commands a premium over future money. People with less intense T.P. will lend to people with more intense T.P. and the fundamental rate of interest will be at the level that clears the market. In addition to the fundamental rate, the interest rate on each type of loan will have components to account for maturity, uncertainty, and changes in the purchasing power of money. For example: the 3-month, treasury bill rate will be lower than the 30-year, BBB rated corporate bond rate.
Here is some data on market interest rates: