If you or your Apple ID previously "purchased" (downloaded for free) macOS High Sierra when it was current, it remains in your tab of the App Store (on an older Mac running a compatible OS version).
Always verify the integrity of any downloaded macOS DMG. Malicious actors often package malware inside fake "High Sierra" installers.
When you download a .dmg file for macOS High Sierra 10.13.1, you are essentially downloading an exact, bit-for-bit copy of the installer. Double-clicking it mounts it as a virtual drive on your desktop, allowing you to run the Install macOS High Sierra.app package inside.
Once the download is complete, the installer will automatically launch. You can find the DMG file in the "Applications" folder.