In Safari for macOS, choose Safari > Preferences and then click Advanced. You can then check next to the Reading List label Save Articles for Offline Reading Automatically. If that option isn't checked, you can also view the Reading List in the sidebar, right-click an item, and choose Save Offline.
With iOS Safari, you navigate to Settings > Safari and swipe down to the bottom, and then tap the switch to on for Automatically Save Offline. If you have that option disabled, which it is by default, you’re prompted the first time you choose Add to Reading List from the Sharing sheet whether or not to save items from then for offline reading automatically.