What distance method did Edwin Hubble use to determine the distance to local galaxies?
Edwin Hubble measured speed of galaxies moving away from using red-shift method and then calculated their distance using Hubble's constant.
Let us blow a balloon, a little first, and mark few dots on this and then again continue blowing it, say at a uniform speed. One will see that dots are also moving away from each other.
In 1929, Edwin Hubble had found that galaxies appeared to be moving away from us and considering the above example, it was obvious conclusion that the universe is expanding too.
Earlier in 19th century Christian Doppler had observed shift in spectral lines toward lower frequency when a light source moves away from an observer. This shift was found to be in proportion to the velocity of the object.
Hubble found that using this the velocity of a galaxy could be expressed mathematically as
So, by measuring the red-shift in a distance one could calculate distance of galaxies.