Okay, so I was in your exact spot last month when my commute turned into a dead zone for data. Figuring out the legit download game can be a puzzle. First thing I do now is check if the app or site I'm already using has a download icon—looks like a little arrow pointing down. Amazon Kindle, Apple Books, and the Libby app (which hooks into your library card) all have it. Tap that, and the book just... parks itself on your device. It's not magic, but it feels like it.
A trickier part is with serialized web fiction on sites like Royal Road or apps like WebNovel. Sometimes the download button is only for 'privileged' members, which is their way of saying you need to pay for coins or a subscription. I got burned once thinking a story was free to download, only to hit a paywall after chapter three. My rule now: I read the first few chapters online to see if I'm hooked, then I'll consider their subscription if the update schedule is solid. For completed works, I often just buy the whole ebook—it's usually cheaper in the long run than unlocking chapters individually, and then you own the file to sideload into any reader app you want.
Format matters, too. If you're downloading EPUB or PDF files from author websites or places like Project Gutenberg, you need a separate e-reader app like Google Play Books or Moon+ Reader to open them. It's an extra step, but you get total control over your library, no DRM worries. Just make sure your device has enough storage; some of those illustrated novels can be huge.