Technological innovations drive the evolution of human societies. The success of innovations depends not only on their actual benefits but also on how potential adopters perceive them and how their beliefs are affected by their social and cultural environment. To deepen our understanding of socio-psychological processes affecting the new technology spread, we model the joint dynamics of three interlinked processes: individual learning and mastering the new technology, changes in individual attitudes towards it, and changes in individual adoption decisions. We assume that the new technology can potentially lead to a higher benefit but achieving it requires learning. We posit that individual decision-making process as well as their attitudes are affected by cognitive dissonance and conformity with peers and an external authority. Individuals vary in different psychological characteristics and in their attitudes. We investigate both transient dynamics and long-term equilibria observed in our model. We show that early adopters are usually individuals who are characterized by low cognitive dissonance and low conformity with peers but are sensitive to the effort of an external authority promoting the innovation. We examine the effectiveness of five different intervention strategies aiming to promote the diffusion of a new technology: training individuals, providing subsidies for early adopters, increasing the visibility of peer actions, simplifying the exchange of opinions between people, and increasing the effort of an external authority. We also discuss the effects of culture on the spread of innovations. Finally, we demonstrate that neglecting the cognitive forces and the dynamic nature of individual attitudes can lead to wrong conclusions about adoption of innovations. Our results can be useful in developing more efficient policies aiming to promote the spread of new technologies in different societies, cultures and countries.