That's easy. We look at the predictions a DM model makes, and then see if the predictions match observations. People seem to think that just because DM does not interact electromagnetically, the DM hypothesis cannot make testable predictions.

Models are quantitative entities – this is physics we're talking about. They almost always have quantitative parameters whose values initially have large uncertainties. We make observations in order to tighten the error bars of those parameters – to rule out parameter values inconsistent with observations.

Now, if we found that two observations are inconsistent with each other – each implies a parameterization incompatible with the other – and could rule out experimental error via repeat experiments etc, then that would be evidence against the entire model. In dark matter's case, we might realize, for example, that we cannot predict both galactic rotation curves and CMB anisotropies with a single DM model. That would be evidence against DM. (But that's not the case, both seem to be perfectly consistent with a single, well-constrained model.)