In a quality coach training program, coaches learn to identify different personalities in the moment and learn to identify different learning styles. This is then further developed with specifics on how to work with each person differently based on what they are thinking and feeling in the moment, and how they are learning, processing, and focusing.
For example, sometimes people are more logical in their thinking and deciding and other times it is driven by emotion.  A coach learns to be aware of how the client is thinking and adjust to that. Sometimes people think inside their head and other times they think out loud. Some people consider others first and others prioritize themselves. A coach is aware of how their client is thinking in the moment and adjusts accordingly. Some people learn visually, others are auditory learners, and others kinesthetically. A coach recognizes which it is and applies the awareness by exploring possibilities in a way that works best for the individual. Additionally, in defining goals, some focus on what they don’t want and the coach shifts their focus to what they do want. If a client is motivated by external considerations the coach explores the internal motivation too. If a client is reactive, a coach asks about proactive options.
Ultimately, co-creating the coaching relationship starts with a coach recognizing what is happening for the client, and then adjusting to it so that the client is comfortable with the coach and with exploring in depth during coaching sessions.