>How do I become better at listening?
Short answer: practice.
Really, conversation is a skill that needs to be learned like any other. If, while you're improving, you need to choose between listening and thinking, then always listen first. There isn't always a need to respond immediately during conversation. The content of your words should matter more than the speed by which they were delivered. If a brief pause will allow you to better consider what has been said, then by all means pause. If you need more time, and the silence may be uncomfortably long, simply acknowledge that you're absorbing the new information. If nothing else, that will demonstrate that you care enough about the speaker to consider their words before replying. Caring about the other party, about their thoughts and perspective, is the real key to being a good listener.