Products: Nintex for SharePoint 2013 and Nintex for SharePoint 2010. For Nintex for SharePoint 2016, see the product help.
This applies to Nintex Workflow and Nintex Forms 2016, Nintex Forms 2013 and Nintex Forms 2010. If videos aren't your thing, I've also included step by step instructions for publishing a Nintex Form below:
Publish your form to the cloud
In the Nintex Forms Ribbon, click the Live Settings button.
Check the Publish to Nintex Live box. Another checkbox will appear, Allow anonymous access. Check this box.
Click Publish in the Ribbon. You will see a list of all the layouts your form is configured for. Click Publish to confirm.
The URL to access the Nintex Form anonymously will be provided to you once you confirm publishing. This URL is the same for any layouts you publish the form to. For example, since I created a form for desktop and smart phone, I can access the form using the URL on both devices.