Using Forms on Anonymous Sites: Create a Contact Form
One of the more common requests I receive is to create forms to enable anonymous users to submit feedback on public-facing SharePoint sites. Chapter 4, “Design Administrative Tasks: Site Settings, Permissions, and Creating Sites,” shows you how to configure anonymous sites and also adjust lists and libraries for anonymous access. This section covers how you can still link to a list form and allow anonymous users to complete the form.
If you are using a SharePoint Server 2010 publishing site and have the lockdown Feature enabled and want to enable anonymous users to access to certain lists or libraries, then you need to either disable the Feature or use a different site or site collection ...