Often when we are with other people, we don't fully experience being with them. Our minds are too busy judging, comparing and making plans. This mental chatter pulls us out of the moment and takes us away from the person we are with.
If you let go of the clutter in your mind, you can be with other people just as they are in the moment. Not only will this be more satisfying to you, but also the people you are with will notice, perhaps on an unconscious level, that being with you feels different from and better than before. Paying full attention is a gift that many people will deeply appreciate. It's a simple way to form strong connections with others.
Try this: Next time you are talking with someone, treat the conversation as a type of meditation. Be aware of when your mind starts to wander, and then gently bring it back to what the other person is saying. Help ground yourself in the moment by using your senses. While still focusing on the meaning of what the other person is saying, take in sensory information about them as well. Listen to the tone and pitch of their voices, and watch their facial expressions.
Be especially aware of the times when you start thinking about what you are going to say next, while the other person is still talking. When you catch yourself doing that, let the thoughts go, and bring your attention fully back to listening.
As in any kind of meditation, your attention will wander in and out. Perfection is not the goal. What matters is the intention of becoming aware of when your thinking takes you away from the moment and away from the other person, and then gently bringing your attention back.