My thought on learning prepositions.

Nearly every preposition has a wide set of meanings and uses, both in English and in Russian. And they never fully intersect. That is what one has to bear in mind.

I would not recommend to learn all the usages of a preposition at once. That would create a mess in your memory, and it is a very ineffective way. Instead of doing that, try to figure out what a preposition means in each specific occasion step by step, do not bother with its other meanings at the same moment. And try to construct some more examples with the same meaning. Repeat them many times until you feel you are getting used to it.

Examples for your case (I tried to make simple ones), all of them use more or less the same meaning of "при" (при + action noun):
При изучении языка необходимо запоминать новые слова.
Будьте осторожны при работе с электричеством!
При покупке билета проверяйте сдачу.
При чтении книги не выключайте свет.
При просмотре фильма не разговаривайте слишком громко.
При повышении температуры обратитесь к врачу.
При пожаре звоните 01.