The only interest rate the Fed sets as a matter of administrative policy is the discount rate. The discount rate in the interest rate the Fed charges banks for loans they take out from the Fed.
The federal funds rate is the interest rates banks charge to other banks for over-night loans. Banks usually take out such loans to meet their reserve requirements. For this reason, the Fed targets the federal funds rate. If it rises (falls), the Fed takes that to mean that reserves are more (less) scarce.
To manipulate the federal funds rate, the Fed buys Treasuries or other assets from banks and pays for them with cash or checking account balances at the Fed. Either of these counts as reserves for the banks. The larger supply of reserves will reduce the banks’ demand for more reserves through federal funds borrowing and therefore, push the federal funds rate down.
With the greater reserves banks can issue fiduciary media and create credit. The additional supply of credit will push interest rates down in the credit markets the banks lend into, like mortgages or prime loans or AAA bonds.
If there was a loss of confidence in Treasuries, the Fed could just buy more of them to prop up their prices and keep their yields low.
Take a look at Murray Rothbard’s book, The Mystery of Banking: