The purpose of the article is to describe the trainings implemented as part of the project "E-Active Residents of the Kuyavian-Pomeranian and Lódz Voivodeships" and to present the results of partial assessment of the level of digital competence of 75 training groups (837 participants) recruiting from selected municipalities of the Kuyavian-Pomeranian Voivodeship (Aleksandrów Kujawski, Chelmza, Lipno, Lubanie, Radziejów, Stolno, and Sliwice). The project is implemented as part of the Digital Poland Operational Program for 2014-2020 by the Pluznica Commune Development Association in partnership with the Polish Ministry of Digital Affairs and the Foundation of Active Development Initiatives. The authors limit themselves to presenting results of 75 trainings only in the municipalities of the Kuyavian-Pomeranian Voivodeship, in which they had conducted the trainings on their own, in the capacity of certified instructors of digital competences, in the period of December 2018-end of June 2019. Each participant of the training was obliged to take a pre-test consisting in 10 single-choice questions, that verified his digital competences (like use of search engines, digital resources, e-administration services, tools of cybersecurity). At the end of the training (consisting of the lecture with the presentation of tools) each participant had to solve the post-test to validate his knowledge (again, 10 single-choice questions with the pass threshold score of 75% of correct answers). Comparing the results of both tests, the authors of this article assessed the level of digital competence of participants' group before and after the trainings. The conducted analyses proved that all the training groups increased their levels of digital competences. In the case of almost 55% of groups, an increase by one level was evidenced (51% for average to high competences, and 4% for low to average competences), and in the case of 35% of groups -- by two levels (from low to high competences). Slightly above 10% of groups increased their already high level of competences that was featured initially. The obtained results are the evidence of the high effectiveness of the trainings. In their final outcome, as much as 72 training groups increased their initial levels of digital competences to the high level, and 3 to the average level. There was no group reported with a drop in the level of competences. The results of analyses indicate high effectiveness of the trainings conducted within the scope of the "E-Active Residents of the Kuyavian-Pomeranian and Lódz Voivodeships" project -- at least with respect to the Kuyavian-Pomeranian Voivodeship. A large number of participants featuring average and low digital competences (89% before the training and 96% after the trainings) may be evidence for the unsatisfactory level of digital competences in Poland. On the other hand, a relatively high interest in the trainings among the seniors (aged 61 or older), may indicate that there is still a considerable need in Poland for initiating actions countering the digital exclusion.