When it comes to mastering the digital world, the education system is more and more facing the task of making students competent and self-determined agents when interacting with digital artefacts. This task often falls to computing education. In the traditional fields of computing education, a plethora of models, guidelines, and principles exist, which help scholars and teachers identify what the relevant aspects are and which of them one should cover in the classroom. When it comes to explaining the world of digital artefacts, however, there is hardly any such guiding model. The ARIadne model introduced in this paper provides a means of explanation and exploration of digital artefacts which help teachers and students to do a subject analysis of digital artefacts by scrutinizing them from several perspectives. Instead of artificially separating aspects which target the same phenomena within different areas of education (like computing, ICT or media education), the model integrates technological aspects of digital artefacts and the relevant societal discourses of their usage, their impacts and the reasons behind their development into a coherent explanation model.