Mirror listening is one way to do this. By pausing to reflect back the messages we receive ("You said X, Y and Z"), we remain present to the person who is sharing an experience without being swallowed by our own. We show the speaker we "got" him or her instead of contaminating his message with our own reactions in the form of interruptions, questions or comments, or any other verbal and non-verbal reactions to what is being shared.
By eliminating reactivity, mirroring connects people in conflict, and tension just melts away. It is very soothing to be heard in this way.
Any thought or feeling can be shared but, if we want to maintain connection to another human being, we must take great care in how we share, using a form that neither hurts nor offends the person we are talking to. (It is in fact the form, not the content, of the message which is most important).
This can be done using I-statements which indicate that we know that everything we share (every thought, impression, feeling or reaction) belongs to me and me alone, and is a mere reflection of my own subjective experience, and not a fact I am imposing on you or something you have to agree with. (Questions and you-statements, i.e. "why are you asking me now?" or "you are talking too much" instantly deflect attention away from me and can create conflict and disharmony, especially when experienced as attacks or criticism, which they usually are).
To show you humbly acquiesce to the reality and separateness of another human experience, it is necessary to both put yourself aside to mirror someone else and use I-statements to describe what is going on in yourself.
There are two sides to good communication: sending and receiving. But the hardest part is humility.