Allowing yourself to believe that an unvalidated feeling, idea or situation is true is self-deception. If your first thought on reading the title of this thread was, “Why should I?” then please explain why you would rather live your life constantly deceiving yourself than accepting reality. I think I know the answer to that, but this thread is for those theists who would rather be intellectually honest.
The first thing we need to do is determine exactly what it is you believe in so please provide a factual description of your God’s characteristics and abilities so that we can be sure that we will know it when we see it. Try to be as specific as possible to avoid ambiguity. We need to be able to differentiate your God from other phenomena. So, for example, claiming that your God is love or the universe or is all around us is not helpful in the least. Claiming that your God is supernatural or beyond the natural, observable universe is also not helpful. If your God is beyond the observable universe then how could you possibly have observed it to conclude that it is real? So again, please provide a factual description of your God’s specific characteristics and abilities.
If you cannot provide a factual description of your God then please provide enough sound evidence and sound arguments to prove beyond reasonable doubt that it is real. I’m assuming that no intellectually honest person would use unsound evidence or unsound arguments to reach a conclusion. Try to avoid using misapprehensions, fallacies or misrepresentations as evidence or arguments. Bare assertions or assumptions are not useful. Please provide evidence and arguments that can be tested and verified and that unambiguously establish your God as the only explanation.
If you cannot provide a factual description of your God or any sound evidence or sound arguments to support your belief then please explain what distinguishes your belief from imagination. Imagination is forming a mental image of something not present to the senses. Something imaginary exists only in imagination; it lacks factual reality. Subjective notions such as internal personal experiences or feelings are indistinguishable from imagination. If you couldn’t turn to people next to you and ask, “Did you see/hear/smell/feel that?” and expect them to say, “Yes” then whatever it is you experienced was likely imaginary. You need to provide something objective that we could all perceive to detect your God and verify that it is real. We need to distinguish objective reality from a subjective reality in which people believe things are as they want or imagine them to be rather than as they are.
Now, if you have provided a factual description of your God or sound evidence and sound arguments to prove that it is real then you have established the truth or validity of your belief. Otherwise, it is more likely you are simply deceiving yourself.
Let me answer this from my previously evangelical perspective, that I have a hard time divesting myself off completely.
If you asked me these questions about 2 -3 years ago, I'd say that from a Christian perspective, God is a being who is beyond human understanding, and so cannot be explained or comprehended by humanity completely. What can be known about God is revealed in the Bible. Namely, that God cannot sin, cannot lie, God is good, etc... Also, the Bible (at least the NT) says that without faith, it is impossible to please God, implying that God expects faith and therefore, will not be provable in a scientific sense, since science is not faith, but knowledge based.
How does a Christian know that God is real? Well, they believe he is. There are some hints to his existence. For example, the abundance of life forms on our planet, the mathematical precision of the observed natural order of the universe, etc.... Granted, Lawrence Kraus has an explanation, but he has a Phd in Physics and his explanation requires a lot of thinking for most people, and it's easier to take an easier explanation that feels right.
And, don't forget the fear factor of Christianity. Christian God had to kill his own son for the sins of the world. While not much can be known about this God, it's clear that you don't want to get on his wrath. So, while not completely understanding this God, it's better to be safe than sorry. Do you want to risk your eternity in hell? If there is no God, a Christian loses very little (talking about a modern, evangelical Christian, not about a 15th century monk). But if there is a God, then atheist loses everything.
I think that most evangelicals would agree with the above explanations. I'm a realatively new ex Christian but the rest of my family is very religious (my dad is a pastor of a Baptist church and I know he would agree with the above).