One of the basic means by which skeptics attempt to deny the possibility of knowledge is the argument from criteria. Rather than combating each case of knowledge individually, this argument aims to establish that knowledge is logically and universally impossible. Of course, a true skeptic cannot claim to know even this, but an individual who accepts logic as viable must acknowledge the skeptic's argument.
The argument depends on the relatively standard definition of "knowledge" as a justified, true belief. Justification requires some sort of evidence, e.g. induction* or the reliability of the Dalai Lama's word. There are only three ways to justify any evidence type e. One can appeal to another piece of evidence e, such as arguing for the reliability of induction by pointing out that it has worked many times before. One can appeal to a different type of evidence, such as asking the Dalai Lama to vouch for induction. Evidence e could also conceivably be confirmed if one could somehow demonstrate beyond doubt that e arrives at the truth.
It happens that all three of these methods of verification cannot be used. Justifying e with e assumes as a premise just what the argument is trying to justify, so it is circular reasoning. Justifying induction by induction would be a fallacy. If one appeals to another kind of evidence, f, to justify e, one must then provide justification for the believability of f. We must ask ourselves on what grounds the Dalai Lama is to be trusted if we would provide his word as support for induction. Whatever justification we use for that must then be justified, and so on ad infinitum or until the justifier falls to one of the errors of the other methods. In order to demonstrate that e arrives at the truth, there must first be some "true" fact or principle that we know absolutely so that we can trace a path to it with e. For that, however, we would need some criteria that confirmed for us the truth of the fact, and those criteria too must be justified by one of these three methods.
So, argues the skeptic, if there is no possible way to justify evidence, then there is no usable evidence to justify a given bit of potential knowledge. Knowledge as it is defined by "justified true belief" is therefore impossible since justification is impossible.
In my opinion, the simplest argument against this form of skepticism is that we may in fact have knowledge; we simply cannot know or rightfully claim that we have knowledge. A person can have a belief which happens to be justified by the evidence he uses to support it, but he will never know for certain whether or not that knowledge is really knowledge. One could argue that this is not really knowledge or that justification the support for which is unconfirmed is not really justification, but this adds an additional criterion for justification which I do not believe is inherent in the original definition of knowledge. The true belief simply needs to be justified by the given evidence; this can arguably be the case whether the knower is sure of the evidence's viability or not.
* Inductive reasoning, i.e. using observed instances to support hypotheses.