A modern library become an information and communication center where visitors have a possibility to work and even rest. The information literacy is very important both in the scientific world and for all categories of users of the universities libraries (students, postgraduate students, scientists) and is necessary for each contemporary researcher. However, we have problems as with understanding of it in the university as for a collaboration processes between librarians and faculties. Some lecturers don't use scientific databases ourselves and don't teach their students to work in the library - for different personal reasons. The low status of the scientific publications and successes of the "predatory journals", unmeant or intentional plagiarism are the results of the situation. The trainings of the information literacy led by the librarians are the solution and there are usually conducted in the different universities in the world now. The librarians from V. N. Karazin Kharkiv National University initiated in 2019 series of special lessons in the collaboration with the lecturers for the all categories of the users. The most popular themes now are - how to use citation and full text databases for students and researches, search and selection of the scientific information in the library, the bibliographic description etc. The individual consultations on the author's profiles in Scopus and Web of Sciences for the researches from both the university and other institutions of higher education of Kharkiv are very popular too. We can see the great interest for librarian's trainings by the scientists from the technical, medical and economical specialties and poor - by them who don't use scientific databases reasonably. In this situation we need to work actively and systematically with the faculties for the common benefits and results.