The states have the option to collect it themselves (and get paid for doing so). If, for some reason, a state chooses not to collect it themselves, the feds would either do it directly, or contract it out (I think the latter is more likely, though neither is really specified in the legislation).
So basically with the States collecting the taxes and sending them to the Federal Government, we are back to the basic inter-level-government tax structure we had in Pre-Civil War U.S., the irony is not lost on me.