There are 4 steps involved if you want to enable SharePoint 2010 anonymous access: First you need to enable it on the web application and after that for the site collection, the master pages gallery and the style library.
Open Central Administration and go to Application Management > Manage Web Applications and select you web application where you want to enable anonymous access. Click
Select the zone where you want to enable it:
Click to enable anonymous access for the web application:
Usually the client integration features are disabled in the same process:
Open Site Actions > Site Permissions and click anonymous access:
A new dialog opens.
Enable it for the entire web site:
After that you should see the following:
Master Pages Gallery
Go to Site Actions > Site Settings > Master Pages and Page Layouts and click the library tab to edit the library permissions:
Enable the access to view items:
Go to Site Actions > Site Settings > Site libraries and lists > Style Library and click the library tab to edit the library permissions
Again enable the access to view items:
Sign out and close the browser. After opening the browser and the site again you are no longer logged in: