We show a laboratory experiment in which students can learn the use of interferometry as a valuable tool in astronomy. We detail experiments based on the use of the classic Michelson stellar interferometer able to reproduce the size of single stars and to characterize double star systems. Stellar sources, single and double, are reproduced by a laser light emerging from the circular end faces of one or two step-index polymer optical fibres. Light coming from the fibre end faces passes through two identical pinholes located on a lid covering the objective of a small telescope, thus producing interference fringes. The measurement of the fringe visibilities allows us to estimate both the diameters of the simulated stars and the separation between them, with errors lower than 18% for a range of light sources that can recreate the apparent size of the outer Solar System planets Uranus and Neptune and the binary properties of the Alpha Centauri system. The exercises here described illustrate the optical principles of spatial interferometry and can be integrated into courses on astronomy, optics or space science, with close interaction between theory and experiment.