In my experience theists usually begin a debate by appealing to standards of evidence we all find colloquially useful in everyday life. They will talk about the reliability of the Bible as a divine historical document, fulfilled prophecy, answered prayers, observed miracles and other claims that can actually be tested by experimental and historical sciences. However once you show them that:
a. the Bible has failed all the tests of a reliable historical document.
b. the Bible only makes self-fulfilled prophesies (i.e. "this took place to fulfill what was prophesied Matthew 21:4-5) or prophecies that correspond with normal probability laws (i.e. Jerusalem will be sacked; there will be wars, etc.).
c. several independent studies of intercessory prayer have proved prayer to be futile (see the STEP Prayer Project).
d. no miracle has been directly observed and verified by others without a natural explanation (i.e. a severed limb supernaturally regenerates).
…they then revert to pseudo-scientific arguments from incredulity. In other words, once they see that real science is no friend to their claims they begin using a bastardized version of science. They make the Cosmological Argument and they invoke the anthropic principle. Using legitimate scientific data they form unwarranted and illegitimate conclusions that life MUST have been implemented by their own god. They believe that pointing out weaknesses in evolutionary theory (something that scientists have been doing themselves for over 150 years) somehow lends more credibility to their god hypothesis. They draw unsubstantiated correlations between the theory of evolution and social darwinism (which, by the way, even if such a correlation was founded on evidence wouldn’t make it untrue). And so on, etc.
Once you show them that these arguments hold no water they revert back to what they should have started with in the first place: faith. This is usually combined with attempts to criticize atheism. This cycle happens almost every time I debate a theist. Science -> Psuedo-science -> Faith -> Denigrating atheism and “scientism.”
When science turns from amity to enmity for the theist things really start getting interesting. One of the things I hear a lot at this point is the paranoid assertion that scientists and/or science itself are biased against the supernatural.
This is wrong for two reasons. First, science itself is completely neutral on this issue. The fact is that supernatural claims lie beyond the purview of the scientific enterprise. The underlying principle of science is methodological naturalism which states that natural phenomenon can only be observed and explained by natural models. This is why science will never prove or disprove all possible gods. Science speaks to improbability, not impossibility. With a theistic god like Yahweh, Allah or Jesus all science can do is evaluate particular claims that occur in the natural world. This would include miracle claims, the effects of intercessory prayer, the historical merit of the Bible, the manifestation of a spiritual being, and so forth. While science cannot say whether or not all possible gods do or do not exist, it can say that the things one would expect to see if particular gods DID exist are simply not observed.
Secondly, if scientists have all conspired together on this anti-supernaturalism bias then why are roughly half of scientists religious? These scientists obviously believe in the realm of the supernatural but rightly understand that they must separate the supernatural, by necessity, from the scientific process because, by definition, it is a process that only works in the natural world.
Some people (I am not one of them) subscribe to philosophical naturalism which states that only the natural world exists in the universe. I am sympathetic to this philosophy. However, because I simply have no way of knowing this, I reserve judgment. In other words, I have no bias against the existence of the supernatural. Methodological naturalism is distinct from philosophical naturalism because it is simply an epistemological way of acquiring information, not a worldview pronouncement.