If this upgrade process is done correctly, then you should find in the Applications folder an app named "Install macOS Catalina". Double-click that and the upgrade should begin. If that app is not there or if the upgrade does not start or if you encounter any error, then at this point I would simply start over.
To start over, first delete any files that you have already downloaded for this exercise. Delete them from the Desktop or the Downloads or Applications folders or wherever it is that you stashed them. If you find any "Install macOS..." applications in the Applications folder, then delete those, too. Finally, empty the trash and restart the Mac.
Now you can begin again. Since, according to your tag line, the computer is already running macOS 10.14 Mojave, there is only a single download that you need. This link will take you right to the correct upgrade installer to be downloaded from the App Store: https://itunes.apple.com/us/app/macos-catalina/id1466841314 (Use Safari to download this, other browsers may not work properly.)
Once that Catalina installer application is downloaded, it should automatically launch and begin the upgrade installation. If it does not launch automatically, then find the "Install macOS Catalina" application in your Applications folder and double click it to begin the upgrade. Then simply follow the prompts through to the end.