The Sanskrit word for compassion, Karuṇā, means to do something to alleviate the pain and suffering of others. It is not pity or sympathy as we might think. Compassion is directly related to acceptance of the way others are. It is directly related also to the lack of judgement and most important to Selfless service.
When we meet someone, we either like the person, judge the person, react to their energy or feel neutral and aloof. When the compassionate energy is stronger within us we are able to stand in the midst of someone's dark energy without reacting (judgement, thinking, arguing, etc). Just being there in present moment full awareness is already creating a transformation towards a lighter energy.
Compassion in itself develops slowly as ones own heart opens more and more, particularly in the self acceptance.
One way of developing compassion is practicing Self Forgiveness. Really forgiveness is just understanding that everything is just the way it is and that we are all part of a unique Oneness, that we are not separate. Self forgiveness is just accepting completely who we are, where we come from, what we do, how we look and what how we feel.
Forgiveness at a physical level is very related to deep relaxation of the body. We do not need to be laying down to be relaxed or to be in deep meditation to be fully relaxed, but that is the way in which we can more easily learn how to relax deeply.
Learning relaxation is one of the most important things one can learn. As Swami Atma in Rishikesh, India says, reeeeeelllllaaaaaaaxxxxx. Very funny when you are in his presence.
If one learns to relax in the physical body, then one has a bigger chance to practice a kinder approach to oneself and to others, which is forgiveness, from which acceptance can arise easier and from there compassion. Compassion feels like bliss, feels like being one with God. Compassion is a delicious experience and it only benefits the Whole.
God bless you much in your path, all the very best always,