Follow these steps to allow anonymous access in SharePoint 2013.
Go to Central Administration -> Manage Web Applications. From there, highlight the Web application and select Authentication Providers.
Click on the default zone and check ‘enable anonymous access’ if not already enabled.
Now click on anonymous policy and select Deny Write.
Open a browser and navigate to your SharePoint site. If you are prompted for credentials, log in as a site collection administrator.
Right click on the cog at the top right and select site settings.
In the site settings page, under Users and permissions, select site permissions.
Click on the Anonymous Access icon.
Select what part of the Web site anonymous users can access.
This will grant anonymous users read only access.