One of the best ways is memorization of poetry and prose. Start with a small volume of poems or passages, gradually increasing the size of the text and complicating it. Prose is harder to teach, so it should go, when a teenager has already mastered poetry. You should check how long the memory remains learned. If he remembered two days later? And in a week? And in a month?
Another way to develop the memory – traditional school a summary and a paraphrase. Let the teenager close to the text retell you read an article or a Chapter from the book. Or write a statement, trying to use as much vocabulary from the text and observing its structure. If you do this regularly, you will improve not only memory, but also speech.
In addition to these traditional, there are special exercises to develop memory, both visual and auditory. For example, say 10 of any words that are not related to each other logically and ask the teenager to repeat everything he remembered.
For training auditory rote memory quickly speak 10 three-digit numbers. The person must repeat them. In this, as in the previous exercise, the norm is 6 generic words or numbers.