It's difficult to develop trust and faith in a teacher unless we put into action what they teach. First of all, we have to investigate into what they are teaching. This is what the Kalama Sutta asks us to do, to investigate, "Is the teaching skillful? Will it lead to benefit or harm to ourselves or others?" We have to use our wisdom as to what they are teaching. It's important not to just get swayed by the teacher's personality or charisma, but to investigate into what they are teaching: Is it skillful? Is it not? Is it beneficial? Is it not?
In the scriptures, the Buddha gives us a way to investigate into the level of another's integrity and wisdom. This is seen "after a long time, not a short time; through close attention, not without attention; by a wise person, not an unwise person." So it's important to visit the teacher in order to understand what they are teaching and investigate into whether it's skillful or not. After you've been with them for some time, if they give good answers to your questions, if you have investigated into whether following their teachings will bring forth beneficial qualities, and if you then do them and it works, you develop experiential confidence and trust in the teacher.
We are very fortunate to have the Buddha's guidance in this to know how to judge. Judge by the Four Noble Truths and the Noble Eightfold Path. Is what the teacher is teaching based in Right View or wrong view, Right Intention or wrong intention, Right Speech or wrong speech, Right Action or wrong action? If you have doubt, go and ask the teacher about it, so that they might give you good reasons and arguments about your concerns.
As far as the teachings, personally, we developed confidence in the teachings first of all. They corresponded to what we had already understood in our lives. When we practiced a teaching, if it actually ended Dukkha, if it actually worked and was practical, then we took it on. As we practiced, we developed experiential understanding and experiential confidence. This built on itself to develop more confidence in the teachings as we tested them and saw them working, so that the initial intellectual Right View of seeing clearly, then went into experiential confidence through the practice, and this is the same as the deepening of wisdom. Often people see the Noble Eightfold Path as a linear thing, but it's more of a spiral, a circle that, through experience, continues to develop and work to deepen your wisdom, which helps in all of the factors of the Path.