Digital competence is a transversal key competence increasingly required by the labour market as well as by the job search process itself, most of which has now shifted online. Individuals who have not developed the most basic digital technology skills are most at risk for long-term unemployment. We argue that to bridge the skills gap of digitally-excluded, unemployed citizens we should create a common understanding of what are the most essential digital competences they require, in particular, to solve their job seeking problems. The resulting conceptual framework should aim to facilitate the design of an elementary but comprehensive practical learning programme through which adult learners can readily develop self-efficacy using digital technologies. To fulfil this need, we provide a holistic framework within which ten essential digital competences for unemployed citizens are identified and contextualised. It is grounded on an analysis of generic digital competence frameworks and existing employability-enhancing digital training initiatives. The applicability of this new "basic digital competences" framework was tested using an iterative process of evaluation with practitioners involved in programmes for the unemployed, and through the design of a challenge-based learning project that provides a practical training model for the implementation of the framework in an integrated and transversal manner.