The COVID-19 pandemic made the most of universities' teaching staff involved in emergency distance learning. Yet, about 80% of the staff was unfamiliar with the distance technologies, especially with the process of distance learning. The previous experience of preparing teachers to distance learning has revealed the presence of significant psychological barriers to synchronous and asynchronous communication. At the same time, the system of refresher training almost does not help due to the excessive workload of teachers. The paper offers an option for training tutors, in which the university teachers are provided with access to general-purpose distance courses created by experts. Teachers register in the distance course "Practicum of the Tutor " where they master the theories and technologies of distance learning and gain practical skills during conducting classes with their students, who are registered in the above mentioned courses. Such training resembles the on-the-job training, which is very popular in Western countries. The " Practicum of the Tutor" course was delivered to 74 teachers. 11 teachers have successfully completed the course, among them 7 teachers have involved 132 students in expert-made distance courses. The research demonstrated the effectiveness of training tutors on the basis of high-quality expert-made distance courses with the participation of their developers and the simultaneous conduction of the learning process with students. The experience of on-the-job training is used to support teachers in the course "Practice of blended learning" during the semester. The results of the student survey were discussed at a Round table at the Institute. The attention of teachers who develop and work with distance courses was focused on the problems indicated in the questionnaire, and the ways to further improve the educational web resources of the Institute were developed.