First check your gnome version:

$ gnome-shell --version
GNOME shell 3.36.4

Then go to location where your downloaded ZIP file, for me its Downloads directory.

cd ~/Downloads/

Get the extension UUID from metadata.json by this command.

$ unzip -c dash-to-dock-micxgx.gmail.com.v68.shell-extension.zip metadata.json | grep uuid | cut -d \" -f4
dash-to-dock@micxgx.gmail.com

Or simply open metadata.json file and copy the UUID value. For me it is dash-to-dock@micxgx.gmail.com.

Create destination directory for the gnome extension.

$ mkdir -p ~/.local/share/gnome-shell/extensions/dash-to-dock@micxgx.gmail.com

Unzip gnome extension file into the directory we made in the previous step, using this command.

$ unzip -q dash-to-dock-micxgx.gmail.com.v68.shell-extension.zip -d ~/.local/share/gnome-shell/extensions/dash-to-dock@micxgx.gmail.com/

Then enable gnome extension with this command.

$ gnome-shell-extension-tool -e dash-to-dock@micxgx.gmail.com

if this warning gnome-shell-extension-tool is depricated, use gnome-extensions instead appeared, use the following command.

$ gnome-extensions enable dash-to-dock@micxgx.gmail.com

Don’t forget to replace the UUID of the extension with the one you want to install.

Note that the $ in front of commands means that this command is run as normal user. but # means that the command should be run as root using sudo.