To measure distances accurately to remote astronomical objects like other galaxies is still a very difficult task. We do it by using different methods at different distance (like rungs in the ladder), and then trying to tie the rungs together whenever they meet.
Distances to nearby stars can be measured by the parallax. Beyond that we need to use the luminosity distance of a standard candle.
The best standard candle available to astronomers today is a Cepheid variable. This type of stars change their brightness with a fixed period, and the brighter the star, the longer the period. Thus, by measuring the period of a Cepheid variable, we can determine its luminosity and thus the distance. Cepheids allow astronomers to measure distance to about 60 million light years, or about 20 Megaparsecs.
1 Megaparsec (Mpc) is 3.26 million light years.
A very new type of standard candles appeared only a few year ago: supernovae type Ia. They can go as far as several thousand Megaparsecs, up to the edge of the visible universe.