How did Edwin Hubble find distances using Cepheid variables as 'standard candles'?
Why not read his original paper? It's fairly short by today's standards, despite being such a monumental turning point in our understanding of the size and nature of the Universe.
In short though, Hubble measured the distance to Cepheid's the same way anyone does. There is a distinct relation between the luminosity oscillation period of the star and the star's luminosity. If he can measure the star's oscillation period with good accuracy, he can derive the luminosity. If he can also then measure the brightness (i.e., how bright it appears to be to him) then he can calculate the distance (since luminosity, distance, and brightness are all related).