I have no experience with Discord, so I can't help directly. You could ask for help from the author of the DiscordIntegrator script by leaving a message on KockaAdmiralac's talk page. Also, you could ask for help by creating a new thread on the Getting Technical forum here at Community Central.
The screenshots have changed since I last updated them.
You should see something like this on the top of the channel list of your server. Click on the server's name.
You should then see something like this. Click on the "Server Settings" option to enter your server settings.
In the sidebar of your server settings there should be something like this. Click on the "Widget" option.
In that section should be something like this. "Enable Server Widget" must be turned on to enable the widget. If you want people to be able to join your server through the widget, you should also select a channel in the "Instant Invite Channel" dropdown. ID of your server is in the green box and you should be supplying it to the DiscordIntegrator template.