It's not only your questions or responses that will determine conversational success, it's how you look, move and react to the play that will also assist you in minimizing conversational stress. Like tennis, conversational concentration is critical to keeping the "ball in play". You must listen deliberately and intently in conversational flow - it's not just about preparing you next question or response. Interrupting the other player can also disrupt their stroke and play. It is normal for your mind to wander - the verbal speed of return conversation is a snail's pace compared to the speed of your brain in processing the information. Don't let this mismatch of pace disrupt your nonverbal actions - eye contact and body movements.
Eye contact is critical - focusing on the other player's eyes will tell them you are interested in what they are saying and it will aid in your listening concentration. Nodding can communicate both interest and encouragement for the speaker to continue on their conversational path. Even looks of intrigue or puzzlement can create a non-verbal clue to the player that you want more information.
Your feelings of comfortable conversation will be contagious to even the most laconic player. Showing non-verbal openness will also reduce your conversational stress. Remember you are looking into a conversational mirror - if they look stressful then likely you are stressful also. Take a deep breath, smile, nod approvingly and focus your eyes - watch what happens immediately.
Over thinking is like "over stroking" and will disrupt your flow. Get your body in control and the flow will come naturally.