DAISY (Differential Algebra for Identifiability of Systems) is a recently developed computer algebra software tool which can be used to automatically check global identifiability of (linear and) nonlinear dynamic models described by differential equations involving polynomial or rational functions. Global identifiability is a fundamental prerequisite for model identification which is important not only for biological or medical systems but also for many physical and engineering systems derived from first principles. Obviously, once a priori identifiability is assessed, the accuracy of the estimates will eventually depend on other different factors, as for example, noise, the paucity of the available data and/or the complexity of the model with respect to the available data. The software does not require understanding of the underlying mathematical principles and can be used by researchers in applied fields with a minimum of mathematical background. We demonstrate the DAISY software by checking the a priori global identifiability of two benchmark nonlinear models taken from the literature. The analysis of these two examples includes comparison with other methods and demonstrates how identifiability analysis is simplified by this tool. It includes discussion of some specific aspects related for example to the role of observability and knowledge of initial conditions in testing identifiability. The main focus of this paper is not on the description of the mathematical background of the algorithm, which has been presented elsewhere, but on illustrating its use and on some of its more interesting features.