From the atheist side comes the following points, stated in a wide variety of forms:
- There is no empirical, verifiable, reproducible evidence for any sort of God that is actually worshiped by any religion on earth (leaving open the question whether some sort of timeless, immaterial, non-interventionist, supernatural being might possibly exist beyond our ability to perceive it in any way).
- The various holy scriptures used by different religious beliefs to justify their faith are all deeply flawed insofar as they have descriptions that are at odds with reality (either readily observed or experimentally verified). These include descriptions of the creation of the world, supposed miracles, historical events, prophecies, etc.
- Therefore, since there is no good evidence to support the existence of God and what little evidence is offered is flawed, there is no good reason to believe in God.
From the theist side comes the following points (again, stated in a wide variety of forms):
- The holy scriptures state that the entire universe was created by God and therefore "God did it" is an all-encompassing explanation for everything in the universe.
- Atheists (or scientists) cannot completely explain every single observed phenomena in the universe and provide exact description of every single historical event or process that led the universe to be the way it is today. And for things that do have a scientific explanation, atheists (or scientists) cannot prove those explanations to be 100% true and accurate in every single case.
- Therefore, since atheists can't explain everything perfectly and theists have a book that lets them use "God did it" as an explanation to explain everything, there's no valid reason to not believe in God.
In other words, theists and atheists are basically having two completely different conversations, and debates between theists and atheists are therefore usually "won" or lost" based entirely on how the debate is framed. If the debate is framed by theists as "who can claim to have a source of All Truth," then the theists are going to win every time since atheists aren't actually making any claims to knowledge. If, however, the debate can be framed as "is there any good evidence to support a belief in God or isn't there," then the atheists have a shot.
The problem comes, however, when theists almost always shift the debate away from their own burden of proof and atheists let themselves be put on the defensive as they try to prove how science has better methods of explaining the universe. Atheists, however, don't actually need to provide an alternative explanation for everything theists claim can be explained by God, and they should really stop letting themselves get drawn into that sort of discussion during a debate. Sure, it's awfully nice that modern science has well-tested and verified explanations for such things like how stars and planets form, how life evolves, etc., but that really has nothing to do with whether or not God exists. Even if science had no explanations whatsoever to explain anything about the world around us, that would simply prove that "we don't know" and not that "God did it." If a theist wants to prove that "God did it," it's not enough to simply point out that atheists don't have a better explanation -- they need to offer compelling evidence that God did, in fact, do it.
Once the debate is shifted away from "atheists can't prove that God didn't do it", it's possible to actually examine and refute any evidence offered by theists to prove that God exists. If they go with the argument from design, point out the flaws in that argument. If they claim their holy book is inerrant, point out all the things that it gets wrong. If they claim that God is required to have absolute morality, point out that the Bible is full of moral laws that no longer apply today and that every single religion interprets God's laws in a different way (not to mention the fact that many atheists perform good deeds while many theists perform atrocious acts, often justified by their belief in God). If they go with a cosmological argument that requires some sort of "creator,"point out how much of that argument depends on creative use of definitions (if you can), point out the inconsistency in claiming that everything except for God requires a creator (if you can make a special case for God, why not a special case for the Universe?), and point out that "proving" the existence of a timeless, immaterial being who -- by definition -- cannot possibly interact with the material world or be detected in any way doesn't really provide evidence of any sort of God actually worshiped by anybody. If they resort to personal anecdotes ("I felt Jesus come into my heart") or so-called "Faith Promoting Stories" ("Little Bobby was lost in the woods and prayed, and then he was rescued!"), point out that anecdotes are not the same as evidence and that confirmation bias let's them ignore all the times Jesus didn't come into someone's heart and heartfelt prayers weren't granted. Finally, if they claim that a belief in God gives them comfort, acknowledge that being comforted by a belief isn't actually evidence for the truth of what is believed.
Shifting how a debate is framed isn't always easy, especially when theists know that the only way to succeed is to avoid having to actually justify their own position. No matter how many times you try to point out that they have no good evidence for what they believe, they will constantly try to get you to provide 100% perfect explanations for everything. And even if you do manage to shift the debate to actually discussing the evidence for God, it can be an uphill battle wading through the mountains of misinformation and, sad to say, outright lies that get offered as evidence that everything in the Bible is literally true or that religious miracles really did occur, etc. If you know your stuff, however, and keep the debate focused on the actual topic, you might just get theists to admit that they don't actually have any good evidence for their beliefs and are relying primarily on faith instead. And that's pretty much as far as you can hope to go, in my experience. After that it's up to the theists (and those those in the audience watching the debate) to decide whether faith is enough to justify the way they choose to live.