You have installed zsh but you don’t see the menu-style autocompletion (where you can navigate the suggestions using the arrow keys on the keyboard)
Open a terminal and run this command:
echo "zstyle ':completion:*' menu select" >> ~/.zshrc
After that, restart zsh (e.g. by typing zsh in the current terminal, but this only has effect on your current terminal session). If in doubt, restart your computer.
Note that the command above only enables the menu-st Pfad: pre yle autocompletion for the current user.
Therefore you will need to execute the command for every user you want to enable zsh autocompletion for.
Alternatively you can enable it for all users if ou have root privileges:
sudo echo "zstyle ':completion:*' menu select" >> /etc/zsh/zshrc