We have carried out a theoretical analysis of the goal-formation problem in the history of psychology. The article reveals shortcomings of empirical means of studying the phenomenon of purpose. We have also proposed the technique of studying the goal setting and goal achievement on the basis of theoretical and experimental research analysis in the field of psychology, of goals and the level of aspirations. The general method, which is a modification of the existing techniques for investigating the level of aspirations, is described in details. The peculiarity of the experiment organization, including the instruction, is explained. As tasks (stimulus material) for studying the goals setting and achievement, tests of general (intelligence, creativity, teachability) and special (motor, technical, mathematical, literary, musical, sporting, etc.) abilities, tests for individual cognitive abilities (attentional, mnemic, etc.), professional tests can be used. This study uses Raven's test. The specificity of the experiment is pointed out. The time needed for solving the problems is indicated in tabular form. The course of the study is explained. The article introduces and meaningfully discloses the characteristics of the process of setting and achieving of human goals. These characteristics are based on specific indicators recorded in the experiment. The calculation of the results in the declared scheme is carried out on the basis of an example representing a particular subject. The particular subject includes a graphical and tabular representation. For consistent and correct calculations in processing the experimental results, the recorded indicators are divided into primary indicators (playing the main role in the interpretation of the results) and secondary ones (used to carry out a supplementary, deeper study of human resources). The primary (main) indicators are height (level), stability, and adequacy of aspirations. The secondary indicators should include the objective rank of intellectual productivity, the indicator of effectiveness of the effort spent to achieve the goal, the effectiveness criteria, assessment of the lability / rigidity of the level of aspirations, etc. All other indicators are regarded as intermediate or additional. On the basis of the indicators obtained in the calculation, a detailed interpretation of the research data is presented, including an example of individual results given in the paper. This allows us to decipher the possibilities of a person in setting and achieving his / her goals in a new way. We also have discussed the objectivity of the technique for its subsequent scientific and practical use and considered the scope of technology application.