Short answers, pulled from the story.
The National Bank Act passed on the 25th of February 1863 and was originally called the National Currency Act. It established national banks chartered at the federal level to create a single national currency.
State banks had minimum capital requirements set at $10,000 while national banks required between $50,000 and $200,000. This difference allowed local bankers to open new branches en masse creating competition against national banks.
State banks increased substantially reaching 15,526 total by the end of the century despite earlier decline from 1,466 in 1863 down to 247 in 1868. The Office of the Comptroller of the Currency became part of Department of Treasury responsible for administration and supervision of national banks.
Hugh McCulloch originally opposed the National Banking Act but eventually organized the Currency Bureau. He personally evaluated applications for bank charters and assisted in design of new national bank notes arranging engraving printing and distribution.
A later act passed on the 3rd of March 1865 imposed a 10 percent tax on state bank notes effective the 1st of July 1866. This high tax rate intentionally set so high as to prohibit further circulation of private notes.