This article describes an approach to teaching the programming basics for the software implementation of numerical methods. This approach was used by the author during the practical sessions in the training course "Working on a computer and programming" for the first-year Faculty of Mechanics and Mathematics students of Lomonosov Moscow State University. In this approach, the student receives the necessary theoretical knowledge and develops practical skills in three interrelated areas. The first area is the theoretical foundations of computer arithmetics. The second area is the implementation of machine arithmetics in the target computer system. As an example of the architecture, SSE has been considered. This technology is implemented in modern Intel processors. The third area is the instrumental programming tools. The examples in the third area are based on the standard library of the C programming language, YASM assembler, GCC compiler and GDB debugger.