F-droid is an alternative App Store, dedicated to open source software.
You have to enable installing apps from "unknown sources" (an option available in the Android menus, no root required), then install the Fdroid application, and from now on you can revert back the "unknown sources" setting, and use Fdroid to search and install FOSS apps, including NewPipe.
On newer Android versions (8+), you have to allow the specific app from which the install is launched (browser, file manager, third party store, ...). In practice, not that different.
You have to enable installing apps from "unknown sources" (an option available in the Android menus, no root required), then install the Fdroid application, and from now on you can revert back the "unknown sources" setting, and use Fdroid to search and install FOSS apps, including NewPipe.