Compassion is the ability to understand where someone else is coming from. It involves, at least temporarily, releasing yourself from your own perspective, so you can see things from an outside perspective. Be it another person, an animal, or even something considered inanimate - like the Earth. Compassion is recognition of anything beyond the self. We must acknowledge that it is present, and accept it as valid in its own right. Even if we disagree with it.
Elements of compassionate behavior include:
Listening
Listening is more than allowing someone to speak to you. It's more than hearing them. Listening is being quiet, still and really being present. Even if it's uncomfortable. Or if you quickly identify an easily resolvable issue, try to hold back on interjecting until they are finished relating their story. For now, just sit, and listen.
Consideration
Thoughtfulness comes in many forms. We can be familiar with another's previous experiences. If not, sometimes we can reasonably predict someone's response to us, or a situation. If so, try to tailor your interactions to what would elicit the most productive reaction; emotional, physical and otherwise. You don't need to bend the truth, just be mindful of what you say and do, and how.
Awareness
Compassionate people recognize signals from others; verbal and non-verbal, positive and negative. Be aware of when someone seems to be shrinking back or becoming upset. Again, adapt your demeanor to what would be most beneficial for both of you. But let go of whether or not they choose to remain engaged in a healthy exchange with you. You can only change you, not others.
Care
Care is a genuine interest in others' health and well-being, and your possible contribution to it. Care doesn't have to mean worry. To truly care for someone being and having the best in life, especially if you two are at odds, is a powerful and sometimes difficult component of compassion. Compassion also means softening yourself to those to whom your heart has hardened.
Validation
How another interprets their situation is valid. But may not be beneficial. To show compassion to another, validate their thoughts, beliefs, values, and especially emotions by letting them know these are OK to experience. But remind them to focus on the values, beliefs, thoughts and emotions that are most beneficial - ones that improve their life, outlook and circumstance, or at least their feelings about these things.
Guidance
Guidance offers another perspective that will help them have a better, more enjoyable life or experience. Guidance doesn't necessarily lead them or push them into what you think is best for them. Although you may have these ideas, and this may be your intent; offer your ideas, don't sell a bill of goods.
Compassion is a skill we can all practice. But it does not mean becoming a chameleon and not showing anyone your true colors. Be true to yourself and what makes your personality unique. But treat others the way you want to be treated. And know, no matter how compassionate you are to others, the favor may not be returned. And your best efforts may go unnoticed. Don't let this phase you. Be compassionate to yourself as well as others and you will begin attracting more of the like into your life.