A private bank. It prints a dollar and either: (1)buys a T-Bill with it through the FOMC, or (2) lends it out through the discount window (only to big banks, not to Americans directlt), or since 2008, buys "toxic assets" with it.
How many dollars are printed is decided by unelected technocrats with no public transparency, oversight or accountability.
What the Fed also does is insure the banks because they are for some ungodly reason allowed to lend out over 10x more money than they have (to increase the money supply, econ textbooks say).
There are a lot of people who have said something between 'the Fed is a welfare system for the rich that steals from the poor' to 'it should be ended,' including Bernie Sanders, Milton Friedman, Aaron Schwartz.
In fact during the Civil War Lincoln actually ignored the banks who were all betting against him. He used the a constitutional right to print money through congress and it worked.
In academia, the groupthink around the Fed is strong. Think stronger than Challenger Disaster groupthink. And they're almost all in favor of it.