In my humble opinion and experience: faith and science don't contradict each other. Faith is needed for science to work and scientific approach is needed to establish the real standing of faith in God and His existence. Let me explain a little.
In the above picture faith and science were dealt separately. But in reality that is not the case. Faith is a prerequisite present in every action. If one carefully observes one's day to day actions, one can find out that mainly all of them (if not all) are based on some particular kind of faith. Example: One gets in to a bus, one has faith, that it will drive one safely to a desired destination. Or: One cooks a meal, one has faith, that it will come out tastefully.
This faith is based mainly upon one's experience, or experience of others. Sometimes even that not. But faith is always needed and present.
Faith (although probably unknown or denied by the majority of scientists) is an integral part of the scientific approach. And on the other side scientific approach is a support for the real and tangible holding of one's faith (be it faith in anything). Following picture illustrates this idea:
In the scientific world one gets a particular idea, which was triggered by one's or others' experience, feeling, observation, intuition... Then follows FAITH, that this idea might be true and FAITH that by following some particular process, experiment, one can come to some tangible results.
In the realm of a particular kind of religious faith the same holds true, or should hold true. One gets an idea, due to one's or others' experience, observation, feeling... For example an idea: Behind each mechanism there is some responsible entity. So behind this universal mechanism there has to be also some universal responsible entity, which can be termed as God. Then follows FAITH. Faith that it holds true and that, following some particular process (in this case some religious system), and performing a specific experiment one comes to some tangible results, speak one will realize the existence of the eternal God.
Now comes the most crucial point: The object of the experiment in any religion is ONESELF. One has to modify oneself, and with the new self one is then able to experience God. As usual, any experiment needs some specific setups, some specific time to be performed, some specific conditions, under which to perform it, etc. In one word, some specific PRICE has to be paid. One has to put the object of experiment under a specific modification, in religious terms: PURIFICATION (of oneself). In terms of religious practices that can mean: restraining from sinful activities, adjusting one's daily activities, performing some austerities, regular meditation, modifing one's diet, etc. Hence, as our own life is very dear to us, the price which has to be paid to for realizing God is much higher in comparism with the usual scientific experiments. Few are ready to pay this price and thus God's realization remains a mystery for the majority of common men.
So the quality and trusthworthiness of some particular religious system can be judged by the following criterium: it has to provide a detailed scientific approach of realizing God. This means clear specification/description of the whole process, from beginning to the end, which includes: intended goal, conditions to be respected, prerequisites to be assured, actions to be performed, intermediate steps together with intermediate results (in order to check if the process is working as described), symptoms of getting negative results, symptoms of failure, etc. That why, religion doesn't remain only something imaginary and sentimental anymore and one can get the desired faith needed to start thinking of performing the religious experiment.
To conclude i again mention, science and faith (including faith in God) can't and shouldn't be separated from each other and should be dealt with and studied conjointly. This approach marks a powerful, trusthworthy and dynamic way of understanding life and the nature of the Absolute Truth.