The Hebrew word for compassion is rachamim.
Before we open the ark in synagogue, we recite the Av HaRachamim. This beautiful prayer is for Jerusalem and reads:
Av HaRachamim (Father of mercies), may You willingly do good to Zion. Rebuild the walls of Jerusalem; for in You alone have we trusted, King, God, elevated and exalted, Master of the World.
The walls of Jerusalem, the walls which surround it and circle it, are made of bricks. Individual bricks. And Jerusalem itself is a place that is not only a center of holiness, a heavenly center, but a place where people reside. Individual people. It is also the soul of Israel, the soul of the Jewish people and those who would see her prosper.
If it weren't for the compassion that Hashem shows us daily, we could not stand; in the same way, the compassion that we show others also helps the world to stand. This literal and proverbial wall cannot stand if the bricks are weak or out of place. A strong wall consists of centered and whole bricks and that can only come through acts of compassion.
"Mercy is an extremely noble trait. It is one of the thirteen traits attributed the Holy One Blessed Be He, as it is written (Shemot 34:6): "Merciful and gracious." All that one can do in cultivation this trait, he should exert himself to do. Just as one would want to be pitied in his time of need, so should he pity others who are in need, as it is written (Vayikra 19:18): "And you should love your fellowman as yourself." --Orchot HaTzaddikim, pg 141
Hashem brings us wholeness and strength through His compassion. So too should we show this to our fellow, regardless of their situation. By building up souls, uplifting those who are lowly, it is like raising walls to be unified and whole.
Practice this simple meditation to heighten your ability to have rachamim by focusing on your desire for the uplifting of those who are lowly.
(Note: For more information on meditative techniques, see the source Jewish Meditation by Aryeh Kaplan.)
A strong wall is made of bricks that fit together properly and are arranged in an order. The difference between "hole" and "whole" is the letter "w". One simple letter defines whether something has a gap or is fully in tact. When someone is struggling, there is a hole in his/her existence. It is our job to raise up that brick, to be part of the healing either by word or deed and restore that brick to the wall and bring wholeness. Our wall of humanity is nothing if any or all the bricks are fallen.
Find a comfortable seat in a quiet place. Close your eyes. Breathing in slowly, allow your stomach to completely inflate which in turn helps your lungs to competely inflate. As you exhale, gently pull your stomach in, squeezing all the air out of your lungs. Deep breathing brings oxygen to your brain and helps clear the mind. Continue breathing until you feel relaxed and feel little or no distractions. Let the noises around you, no matter how small, filter out. Focus on your breath.
Honing in on the image of a wall in your mind, imagine you are the brick which is next to a hole in the wall. Imagine you have always known the presence of the other brick next to you and suddenly it is missing. You seek out the lost brick which has always been next to you.You discover it has fallen to the ground below. This is how you should view those around you who need compassion: as if they have fallen and need recognition. Someone else's struggle needs to be important to us. Whether or not you can put them back in the wall, you should try and offer compassion as a form of help.
As you slowly continue breathing, either recite in your mind or out loud:
Av HaRachamim, may You willingly have mercy on...
(insert name of someone you know who is struggling here)
Keep your focus on this phrase as you contemplate firstly someone with whom you are close who is struggling.
Then, allow yourself to confront in your mind someone with whom you are at odds and is struggling, no matter where he/she is in the world. Repeat this phrase with true compassion for his/her situation. Truly reach out in your heart and be sincere in your meditation for his/her well-being.
As you go through these groupings, try and recite this phrase until you feel the same level of rachamim for those with whom you are at odds and those with whom you are close. Hashem is merciful to all and wishes for all to be whole.
When you are finished with your rachamim meditation, slowly open your eyes. Carry these meditations in your heart throughout your day and continue to remember those in need, as well as seek out others who have fallen.
The goal is to create the same level of feeling of compassion for all, as Hashem has rachamim for each one of us. Practice this meditation often so you can begin to display your rachamim more freely.