It is important when arguing with theists to know a bit about formal logic--in part because it gives you the high moral and intellectual ground and in part because the religious pervert the rules of logic so often. One of the things an atheist should know is how to spot and categorize an illogical argument.
There are two primary measures by which the merits of an argument should be judged: Validity and Soundness. An argument is valid if it follows the rules of logic. It is sound if the underlying factual assumptions are true.
Thus, if one assumes as an underlying premise that the moon is made of cheese, then one can make a logically valid but unsound argument that the United States did not send men to the moon. The argument would go like this: The United States claims it sent men to the moon. As proof these men brought back rock samples from the moon. If the men had actually been to the moon, they would have brought back cheese samples. Therefore, the United States did not actually send men to the moon. This argument is logically valid but it is unsound because it is based on a false factual premise.
A logically invalid but sound argument can be demonstrated if one assumes that the moon is made of rocks and dirt. The argument might go like this: The United States claims it sent men to the moon. As proof these men brought back rock samples from the moon. I haven't seen those rocks myself. Therefore, the United States did not actually send men to the moon. This argument is sound because it is based on facts but it is logically invalid because it is based on a fallacy and that fallacy is the notion that speaker and his examination of the evidence are necessary for the conclusion to be true.