Help me to be compassionate.Watch
Place yourself in situations which require compassion, or at least require you to see others suffering. Volunteering at a hospital or a homeless shelter will introduce you to many scenarios which require compassion and empathy leaving you no choice but to develop it. These are also places where many naturally compassionate people will be drawn to so you will be able to watch them and if you fail at developing your own compassion at least you'll be better able to mimic it.
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The desire to be compassionate rests, I believe, primarily on empathy. A person needs to care about other people enough to be moved to want to make a difference to them. I think that empathy's tremendously important, so I've tried to cultivate it myself, mostly by paying more attention to the way I feel and trying to open up to become more emotionally affected by the situations of other people - both real and fictional. I think that placing an emphasis on empathising and feeling for others is enough to stimulate yourself in that direction.
However, wanting to help people isn't enough - a person needs to have the power and capability of doing so. To that end, it's useful to have skills and mentalities that help in that regard. For example: taking note of the actions of others whom you recognise as worth emulating and incorporating aspects of their behaviour into your own; considering methods to help others regularly; noticing and assimilating patterns of speech that have a positive impact on others; identifying small things you can change about your daily routine that facilitate compassionate behaviour; determining for yourself a code of conduct that requires you to maintain a certain standard of character. These are all things that I have attempted and can recommend to you.
Of the two, the latter aspect is what I personally find most difficult. It's one thing to want to be able to help someone, but another to know the best means of doing so. It often requires a degree of social confidence and self-discipline, or else it is very easy to fail to intervene when in hindsight you wish you would have. These things can be developed in tandem. In fact, by living according to rules that you set for yourself, you can improve in all measures of the virtues you admire - not just compassion.
Best of luck with your self-improvement venture.