I’ve written about both “faith” and “prayer.”
Are they really two different things?
In Judaism, there’s actually no strict definition of “faith.” In some places, it means an attitude of trusting G-d (emunah/bitachon). In others, it means a series of things we believe about G-d (using the Hebrew plural “emunot”). The Talmud more than hints about the peace-of-mind that accompanies sincere faith, but doesn’t dwell on it in quite the way that medieval and Hasidic writings do.
Parenthetically, Christianity, too, has various definitions of “faith.” For Catholics, “faith” includes belief in the Divinely-given authority of the Church. In at least some Protestant writing, it seems to mean “accepting Jesus as a personal savior.” Interestingly, “faith,” in the Gospels, seems to mean an unwavering attitude that whatever you declare in prayer can and will be accomplished by G-d — for example: “If anyone says to this mountain, ‘Be lifted up and thrown into the sea,’ and does not doubt in his heart, but believes that what he says will happen, it will be done for him.” The opposite of such faith, doubting, is elsewhere termed being “double-minded.” 
In any case, I take faith to generally mean an attitude of trusting G-d that’s accompanied by a “letting go” of concern about the outcome of particular events or problems. All the different reasons for faith lead (or should lead) to the same cognitive act: “letting go.” Members of different religions might not agree on why we have faith, but when we compare our experience of faith, we find common ground that is both wide and deep.
There are certainly people who say they “trust” G-d. But even meant sincerely, if they continue to be worried or fearful about outcomes, I’d say that although they have an idea of faith, it’s not being expressed in their hearts. When faith is in and from the heart, there’s no question of worry or fear.
Getting to that place of “letting go” isn’t an intellectual or rational step at all. Intellectual/rational thought might lead us to letting go, but it’s neither an absolute prerequisite nor a guarantee. The capacity for intellectual/rational thought is one part of the mind. A relatively small one, actually. “Letting go” brings us to a far wider mental field.
The “letting go” must take place. When it does, it’s easily recognizable by the peace-of-mind (peace-of-heart, really) it brings.
The source of that peace is G-d’s own Peace, present in us as our own higher Self. When we “let go,” our attention actually shifts from our own thoughts, feelings, etc., to the unchanging Source of our very life. We don’t necessarily experience it as something other than ourselves; rather, it’s our “Self” unmixed with mental/physical/emotional perceptions.
For myself, I’ve found this mostly in personal prayer. My “hitbodedut” isn’t usually in a forest. In fact, the beauty and peace of the forest can sometimes distract me from the prayer; I enjoy it too much. Often, I’m lying down on my bed, or sitting in a chair. Surrounding quiet isn’t absolutely necessary, but it’s preferable. Even on subway trains during crowded “rush hours,” I’ve been able to pray deeply (especially when seated).
Experience with “visualized prayer” taught me that the mental image doesn’t create the outcome. If it did, the outcome would be the result of will-power alone. The outcome specified by the mental image is created by an Infinitely creative Source, not by the human mind that is forming the image. In visualizing, we allow an outcome to appear. In this sense, the Gospel teaching might be understood: If one tells a mountain to move, and believes that G-d can, will and is doing it, the mountain will move.
In learning to practice this kind of prayer, we might declare an outcome — and then immediately hear our own thoughts: “That’s impossible!” or “That’ll never happen!” or “I don’t deserve it,” etc. Hence the term “doubleminded”: Our mind vacillates between affirming and doubting. In the English-language idiom, we are “of two minds.”
We can learn through experience to disregard these thoughts in such a way that they cease to be real to us at all. We don’t “create” with visualization. We “watch it being done;” it’s as real — more real, actually — than things that we see with our eyes or hear with our ears.
In any kind of prayer, the operative element is “letting go.”
Even in Jewish liturgy, “letting go” is represented by the “hatima” — the final sentence, beginning with “Baruch…,” that concludes every blessing (especially with reference to petitionary blessings). It’s also indicated in “Adon Olam”: “B’yado afkid ruchi” — “I place my soul in His hands.”
We emerge from such “letting go” with increased “faith,” too.
A “faith” based on — and accompanied by — personal experience of the Peace that’s found by “letting go.”
 Mark 11:23