Practice of the other three Brahmaviharas Metta has received plenty of attention and focus of practice. Even a search of Buddhism SE shows over 170 posts with the word "metta" in it.

Comparatively, the other three Brahmaviharas are not so often discussed or focused in similar depth.

How do we practise them?

What are the benefits that can be gained out of the practice?

Canonical quotes appreciated. Theravada preferable, but answers from the perspective of other traditions are also welcomed.
The practice of the Brahmaviharas is comprehensively dealt in Chapter IX of the Visuddhimagga. Online resource :- Visuddhimagga.

Daniel Ingram says that the Brahmaviharas are:


  
  Loving-Kindness (Metta): the natural well-wishing for one's self and all beings.
  Compassion (Karuna): the natural wishing that the suffering of one's self and all beings will cease.
  Sympathetic Joy (Mudita): the natural appreciation of the successes, good fortunes and joys of ourselves and all beings.
  Equanimity (Upekkha): the feeling of peace that comes from realizing that all beings are the true heirs of their karma and that their well-being depends on their actions, and not on our wishes for them.
  


He makes an important point that all the Brahmavihara practices share common ground - they are rooted in conscious intent. In this way they produce positive effects. The structure of the meditations are similar and it is merely the intent that changes, encapsulated by the meaning of the phrase that is used. As in Loving-Kindness meditation, so in the others we (substituting the appropriate pronoun in the blank spaces) we silently intend:


  
  For Loving-Kindness: May _____ be happy. May ____ be peaceful.  May _____ be safe. May _____ live with ease.
  For Compassion: May _____ be free from suffering. May their suffering finally cease.
  For Sympathetic Joy: May the happiness and good fortune of _____ always increase.
  For Equanimity: ____ is/are the true heirs of their karma. ____'s happiness depends upon their actions and not upon my wishes for them.
  


Quoted from integrateddaniel.info