Tap the download button on any ringtone. The MP3 file will save to your Files app.
Find the downloaded MP3 in your Downloads folder or iCloud Drive.
Press and hold on the MP3 file until the menu appears, then tap Share.
Choose 'Use as Ringtone' from the share menu. Your new ringtone is now available in Settings > Sounds & Haptics > Ringtone.
Older iOS versions require the GarageBand app to set custom ringtones. See Apple's official guide:
Apple GarageBand Guide