The Transcendental Argument for God, commonly known among apologists and anti-apologists as TAG, is a fairly simple argument at its core but can come in a variety of forms. I will simply address the general argument here. TAG goes as follows. With out god, we can not know anything. We can know things. Therefore, god exists.
The primary flaw is in the first assumption. Our brains are a function of evolution. This can be and has been demonstrated. Our ability to reason is also not unique to humans. Most animals can reason to varying degrees.
However, TAG does make a single valid point. We assume that we are able to learn about our environment; we assume that our group perceptions are a reliable predictor of reality. However, we believe this because that is what the evidence indicates. We do not need to assume that our ability to reason is accurate or even correct to notice that it is useful. Furthermore, to be able to use the TAG argument reasoning must be assumed to be correct to begin with. Hence this becomes a moot point.
Another error is the assumption that we can know things. We actually can not say definitively that we know anything. We make assumptions about knowledge based on our experiences. If I drop a rock I know that it will fall because all evidence indicates that is what will happen. However, could I be incorrect? Of course. As such, knowledge, in the definitive manner used in TAG, can never be achieved.
Since both assumptions that the conclusion is based upon do not hold up, the conclusion based on those assumptions is unsupported.