Despite restrictive measures adopted by many governments worldwide, nicotine addiction remains a serious global health problem. In recent years, adolescents and young people have been strongly encouraged to use nicotine-containing products (NCPs), as the market has seen the emergence of new nicotine delivery vehicles such as electronic cigarettes (e-cigarettes). This study aimed to analyze the patterns of use of NCPs by students. We surveyed 866 young people using standardized questionnaires, including the WHO Global Youth Tobacco Survey (GYTS) and the Fagerström Test. Over the course of their lives, 65.6% of respondents (n = 568) had consumed NCPs. E-cigarettes are the most popular product among current users (31.5% of respondents, n = 273), ahead of traditional cigarettes and hookahs. A significant portion of users (67.3%, n = 233) combine several types of NCPs. The median age at first nicotine use was 16.0 [14.0–18.0] years for boys and 17.0 [15.0–18.0] years for girls; among adolescents who had ever tried nicotine (n = 256), 44.4% reported e-cigarettes as their first product. High nicotine addiction was identified in 22.5% of users (n = 78). The main reason for the first try is curiosity (63.5%, n = 366), and continued (current) consumption is mainly motivated by the desire to relax and get distracted from problems. The results of this study emphasize the need to develop targeted prevention programs that take into account current trends and psychological mechanisms of formation of addiction in adolescents and youth.