How is the Hubble constant determined from gravitational waves?
If you measure the gravitational waveform from an inspiralling binary, you can at any point measure the amplitude, instantaneous frequency and the rate of change of frequency. The last two give you the "chirp mass", which is related to the product and sum of the binary component masses.

The amplitude of the gravitational wave then depends on the chirp mass and the distance to the source. Thus we can estimate the (luminosity) distance.

If we then know the redshift of the source, or at least the redshift of the galaxy it is in, then an independent estimate of the Hubble parameter is possible. Therefore this can only be done for gravitational wave sources with identified host galaxies (so far this can only be done for GW sources that show an electromagnetic counterpart - merging neutron stars).

It is a bit more complicated than this, because the amplitude also depends on the inclination of the binary orbit to the line of sight. Fortunately, this can be constrained by measuring the relative amplitudes of the two possible gravitational wave polarisations (+ and ×) and this can be done if you have two interferometers with different orientation of their arms (like LIGO and VIRGO for example), which also helps to locate the GW source in the sky to look for electromagnetic counterparts.