Abstract Astrometry is one of the main pillars of astronomy, and one of its oldest branches. Over the years, an increasing number of astrometric works by means of Hubble Space Telescope (HST) data have revolutionized our understanding of various phenomena. With the launch of JWST, it becomes almost instinctive to want to replicate or improve these results with data taken with the newest, state-of-the-art, space-based telescope. In this regard, the initial focus of the community has been on the Near-Infrared detectors on board of JWST because of their high spatial resolution. This paper begins the effort to capture and apply what has been learned from HST to the Mid-InfraRed Instrument (MIRI) of JWST by developing the tools to obtain high-precision astrometry and photometry with its imager. We describe in detail how to create accurate effective point-spread-function (ePSF) models and geometric-distortion corrections, analyze their temporal stability, and test their quality to the extent of what is currently possible with the available data in the JWST MAST archive. We show that careful data reduction provides deep insight on the performance and intricacies of the MIRI imager, and of JWST in general. In an effort to help the community devise new observing programs, we make our ePSF models and geometric-distortion corrections publicly available.