Currently, the use of hyperspectral imaging (HSI) for the inspection of microscopic samples is an emerging trend in different fields. The use of push-broom hyperspectral (HS) cameras against other HSI technologies is motivated by their high spectral resolution and their capabilities to exploit spectral ranges beyond 1000 nm. Nevertheless, using push-broom cameras in miscroscopes imposes to perform an accurate spatial scanning of the sample to collect the HS data. In this manuscript, we present a methodology to correctly set-up a push-broom HS microscope to acquire high-quality HS images. Firstly, we describe a custom 3D printed mechanical system developed to perform the spatial scanning by producing a precise linear movement of the microscope stage. Then, we discuss how the dynamic range maximisation, the focusing, the alignment and the adequate speed determination affect the overall quality of the images. Finally, we present some examples of HS data showing the most common defects that usually appear when capturing HS images using a push-broom camera, and also a set of images acquired from real microscopic samples.