We can estimate the distance of the nearest objects to us in the Universe by measuring the shift in their position relative to the background stars as the Earth moves around the Sun (parallax),
The distance to more distant objects can be estimated using the known relationship between luminosity and period for a class of stars called cepheid variables, and more distant objects too can be placed by using supernovae – a certain class of which explode with a standard brightness and use the relationship
where
is the intensity of the received light on Earth. Ultimately we can use the redshift,
which expresses the velocity of objects in terms of the a change in wavelength due to the expansion of the Universe:
then use Hubble's Law
to find the distance.