I have written before about the importance of empathy which includes showing concern for others thoughts, feelings and emotions. Listening more and exposing your feelings to another are a few ways someone will see you care about them.
It appears empathy is critical to getting people to believe you are on their side. The next step is taking action to alleviate a situation that someone is having difficulty doing by themselves. Follow through on what you say you will do. A recent example might shed some light on the powerful impact of empathy combined with capability to take action. We had a sick neighbor who just got home from the hospital and was quite weak. We expressed concern for their not feeling well and said we would like to bring dinner over to make their situation easier. We delivered a hot healthy, home cooked meal and everyone was happy. I believe that happiness translated into a speedier recovery The combination of empathy and doing as you say leads to positive results.
After all it is not just the heart that works alone, it has to merge with the mind.