To keep locked onto the floppy data signal, floppy drive controllers used something called a PLL or Phase Locked Loop. This is an essential electronics component that is found in all sorts of things from televisions to washing machines. They are ubiquitous.

The original IBM floppy controller implements a PLL via a pair of 70's vintage Motorola chips. One is a phase comparitor that takes a 500Khz reference clock and the raw, squared data signal coming off the floppy. The chip emits a voltage proportional to the difference in phase between these clocks.

This is filtered and then fed into the other chip, a voltage controlled oscillator. This adjusts the clock speed used to expect a bit of data on the floppy. Essentially, the entire disk can be divided up into little time slices or 'bitcells' in which we expect to read a flux transition (a 1 bit) or not (a 0 bit) and the offset of a bit within the slice or 'window' is used to slide the subsequent windows around, always trying to keep the bits centered.