On my publishing page, I have a button to allow users to add new entries to a list. By clicking the button, a popup box displays a NewItem form of the list.
In order to allow users to have permissions to see the form and add an item to the list, I needed to apply the following steps.
1. Go to the list, select the “List” tab -> “List Permissions” from the ribbon.
2. Select “Stop Inheriting Permissions”
3. Select the permission group and choose Edit User Permissions to give the group “Contribute” permission.
4. Go back to the list. Go to List Settings -> Advanced Settings
5. In the Item-level Permissions section, choose Create Items and edit items that were created by the user