Real-time measurements are becoming feasible in cosmology, where the next generation of telescopes will detect the temporal change of redshifts and sky positions of individual sources with a precision that will allow a direct detection of the cosmic expansion rate. These detections of cosmic drifts of redshifts and positions are likely to become cornerstones in modern cosmology, where one has otherwise relied on the indirect inference of cosmic expansion by estimation of the slope of the fitted distance-redshift relation. Because of their ability to directly detect the cosmic time-evolution, real-time measurements are powerful as model-independent probes. We develop a cosmographic framework for analysing cosmological redshift drift and position drift signals without knowledge of the space-time geometry. The framework can be applied to analyse data from surveys such as the Gaia observatory, the Square Kilometer Array (SKA), and the Extremely Large Telescope (ELT). The drift effects are distorted by the regional kinematics and tidal effects in the cosmic neighbourhood of the observer, giving rise to non-trivial corrections to the well known Friedmann-Lemaître-Robertson-Walker (FLRW) results. We discuss how one may concretely implement the framework in the statistical analysis of real-time data, along with assumptions and limitations that come with such an analysis. We also discuss the geometrical information that can ideally be extracted from ideal high-resolution data of cosmic drifts in combination with distance-redshift data.