Note: If you're using Firefox with the Facebook Container extension enabled, you will not be able to authorize the widget as the extension will block the Facebook and Instagram login URLs. To fix this, follow this tutorial to add SnapWidget to the container.
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When clicking on the Username field in the widget setup screen you should see an authentication pop-up from the service you are creating a widget for.

The pop-up will allow you to log in with your relevant account.

If you do not see the popup display, please make sure that your browser is not blocking pop-ups from https://snapwidget.com

Here is some info about unblocking pop-ups in most major browsers: https://www.isc.upenn.edu/how-to/configuring-your-web-browser-allow-pop-windows