Close stars usually by stellar parallax (http://en.wikipedia.org/wiki/Stellar_parallax), measuring the angle the object moves against the background (really far away objects) as we ourself move about a known distance (i.e. around the Sun). For stars (and galaxies) further away we can use various methods that have been calibrated against each other known as a distance ladder (http://en.wikipedia.org/wiki/Cosmic_distance_ladder). For instance Cephid variables cause the star to pulse (change in luminosity) at a rate that is proportional to their luminosity. If we can measure the rate we can derive the absolute luminosity (the apparent luminosity of the star if it was placed 10 parsecs away). If we then measure how luminous it appears to us from Earth (apparent luminosity) we can work out how far away it is by using pretty simple equations. Cephids are most useful for measuring distances to distant galaxies.

well...it's possible for the twins to be born around the same time but on different days. twin 1 could be born on Tuesday just before midnight and twin 2 just after midnight (i.e. Wednesday).