Making green fire involves mixing borax with ethanol and setting it alight in a pyrex/borosilicate vessel (normal glass will just crack and shatter from the heat).
This is just like a great big flame test. When boron compounds are heated, electrons absorb a certain amount of heat energy that causes them to jump to higher energy levels. After some time, the electrons lose this energy and fall back down to their original levels, emitting this energy in the form of light. Because the energy absorbed by electrons is different per element, each element will give a different colour. Boron gives a bright green colour. Any other colours such as orange and yellow are probably due to impurities in the mixture such as carbon.