I am a person of faith and hopefully I live my life by faith (though it isn't a blind faith that asks no questions). The most famous biblical passage dealing with faith is, of course, Hebrews 11, which offers a definition. "Faith is the assurance of things hoped for, the conviction of things not seen." If you have sufficient evidence, beyond the shadow of a doubt, that something is in fact true and incontrovertible, then obviously this isn't what's in mind here.
I'm a fairly rational person. I ask lots of questions, know that doubt is something I have to deal with, and accept the reality of the gray areas of life. In fact, it is the gray areas of life that require faith. The world of fact is black and white, but life is full of gray. Moving forward in the midst of the gray, of course, requires faith.
When it comes to matters of faith, I rarely have doubts about the existence of God. I do, however, have questions about how we are to understand the nature and character of God -- for instance.
But faith impacts us most clearly in how we lead our lives and make decisions. I will soon be faced with making a decision about where to live and where to work. That decision will likely involve much faith on my part. If faith is ultimately a matter of trust, then I will need a lot of it. I'm in a city far from home, in an area I've never been before, looking at a church that has great potential, it's share of red flags, and tremendous opportunities for ministry. To come here, if they should pursue me and I decide to pursue them further will require that I take a tremendous leap of faith. I may not make this choice. I may choose to stay closer to home, remain with the church I know and love, believing that while safer, it offers it's own opportunities. In the end, no matter the choice, I will have to act in faith.
I think this is the "evidence" of God's presence, that one can have peace in the midst of critical life decisions. I'll let you know how things work out! In the mean time, I continue to live by faith.