The widget code needs to live some where in between the body-Tags of your website.
All required information for this can be found within the admin settings of your Zammad installation.
When testing the functionality of your chat, ensure to have the chat function enabled within the backend and at least one active agent with activated chat function available. Otherwise Zammad will not display the chat.
Sorry, but I already gave the answer to that question.
The rest highly depends on your website and that’s mostly out of scope to tell you were exactly to place it.