This article is the study of the conceptions for optimization, rationalization and constructivism in foreign-language training of students of non-linguistical universities and teaching reading foreign texts in particular. The aim of the research is to formulate the techniques of quick retrieval and understanding of specific information from a foreign authentic text by the students of non-linguistical universities when reading. The scientific novelty consists in the definition of the techniques of quick retrieval and understanding of specific information from a foreign authentic text by poorly motivated or poorly trained language learners. In particular, it is suggested to use a preparatory stage which precedes directly the foreign language reading process. The examples of preparatory stage realization are given. As a result, the feasibility of applying training techniques of quick retrieval and understanding of specific information from a foreign authentic text is substantiated. It includes the understanding of the title of a text, taking into account linguistic pillars such as nouns, verbs and lingua-cultural vocabulary and using a preparatory stage in reading process. The preparatory stage implies the linguistic analysis of syntax constructions and morphological forms used in authentic texts for improving training of students of non-linguistical universities to read texts in a foreign language.