How can banks break themselves up? If they refuse to how can the federal government force them to break up or break them up themselves?
This is an interesting question. The banks themselves will not naturally divide themselves. There are great returns to scale in banking, and risk can be greatly diversified by being massive and having more clients in different positions.
This means they would have to be broken up legally. So, one would need legal cause to break them up, of which at the moment I can think of none that seem to strongly apply. One would likely need a new law. Perhaps they are violating an anti-competitive clause, eg. they are monopolies. (This would require quite a radical new interpretation of the existing laws, though.)
If this is the case, the Federal Trade Commission and Department of Justice generally have purview over past monopoly-busting activity. They bring suit against the company in question and these suits can eventually lead to breaking up a firm.