Both Sierra and High Sierra are available for download through the App Store
Open the Safari browser (Firefox will not work) and click on the links below,
How to upgrade to macOS Sierra - Apple Support
How to upgrade to macOS High Sierra - Apple Support
In each case go to Section 4 and click on Get macOS Sierra or Get mac OS High Sierra.
You will be redirected to the App Store which will open the download page for
the OS selected. It should say 'Get' or 'Download'.
High Sierra is straight forward it downloads the Install macOS High Sierra.app to your Applications folder.
Sierra is different, it is downloaded as InstallOS.dmg to your Downloads folder.
Double-click on that and it will open to InstallOS.pkg.
Double-click on that and an installation window will open,
this does not install Sierra but creates the Install macOS Sierra.app in your
Applications folder.
You can of course upgrade directly to High Sierra.
Before upgrading make a full back up of your Mac.
Check that third party apps you use have updates available for the new OS.
https://roaringapps.com
Check that your printers/ scanners etc have updated drivers and software available for the new OS.
Connect your mac to your router via cable rather than rely on WiFi.
Do not use your mac while it is downloading
and do not use any other devices that share the same internet connection.
If the App Store says Open then it is detecting a previous download of the install app
go to the Applications folder locate Install macOS High Sierra.app.
Move it to the Trash, empty the Trash.
Restart, click on the link again, the App Store should say ‘Get' or 'Download'.