To have a script run from a toolbar, you must first create a command from the script. There is good documentation on this. The following statement summarizes this process well:
Under Executing Scripts:
The ideal way to access a script's functionality however, is where it is integrated into Altium Designer's GUI as a menu or toolbar command. This is normally a two-step process; implementing a script as a Command (with optional shortcut), then assigning the Command to a Menu (static or pop-up) or a Toolbar.
Be sure to read Script as a Command and Create a Command for details on getting from script to command.
Further down the page, the section Assigning Menu Commands gives you the steps to add the command to a toolbar:
To assign a custom command to the PCB editor's main menu or Toolbar menu for example, open the Customizing PCB Editor dialog, locate the custom command and drag it to the desired menu location.
Once you've created a custom command, don't forget that you can assign a keyboard shortcut, which in my opinion would be a further improvement so that a button click is not necessary.