Context. The second Gaia.data release (Gaia DR2 ) provides precise five-parameter astrometric data (positions, proper motions and parallaxes) for an unprecendented amount of sources (more than 1.3 billion, mostly stars). This new wealth of data will enable the undertaking of statistical analyses of many astrophysical problems that were previously unfeasible for lack of reliable astrometry, and in particular because of the lack of parallaxes. But the use of this wealth of astrometric data comes with a specific challenge: how does one properly infer from these data the astrophysical parameters of interest? Aims. The main - but not only - focus of this paper is the issue of the estimation of distances from parallaxes, possibly combined with other information. We start with a critical review of the methods traditionally used to obtain distances from parallaxes and their shortcomings. Then we provide guidelines on how to use parallaxes more efficiently to estimate distances by using Bayesian methods. In particular also we show that negative parallaxes, or parallaxes with relatively larger uncertainties still contain valuable information. Finally, we provide examples that show more generally how to use astrometric data for parameter estimation, including the combination of proper motions and parallaxes and the handling of covariances in the uncertainties. Methods. The paper contains examples based on simulated Gaia data to illustrate the problems and the solutions proposed. Furthermore, the developments and methods proposed in the paper are linked to a set of tutorials included in the Gaia archive documentation that provide practical examples and a good starting point for the application of the recommendations to actual problems. In all cases the source code for the analysis methods is provided. Results. Our main recommendation is to always treat the derivation of (astro-) physical parameters from astrometric data, in particular when parallaxes are involved, as an inference problem which should preferably be handled with a full Bayesian approach. Conclusions. Gaia will provide fundamental data for many fields of astronomy. Further data releases will provide more and more precise data. Nevertheless, for full use of the potential it will always be necessary to pay careful attention to the statistical treatment of parallaxes and proper motions. The purpose of this paper is to help astronomers finding the correct approach.