There isn't one answer to this question: there are many indigenous people, and each of the different groups adapts differently.
But some examples are:
-using technology to transfer and preserve their culture, for example recently an indigenous-themed video game "Never Alone" was released.
-they used modern structures to learn and teach their languages (bilingual teaching in schools)
-they use the possibility to print books and magazines in their languages.
-they adapt their art to modern art, making objects that can be used today, but which draw inspiration from their culture.