Create a Custom Field

I've read in the instructions that you should be able to create your own custom fields. In the Customization section you click on the "fields" tab. Then you should be able to click the "New Custom Field" button which is next to the "Map Fields" button and the "Map Dependency Fields" button. I do not see a "New Custom Field" button. We really need a "Company Name" Field in our "Contacts" Tab section. There is only a contact name in the Contact information section. I am the administrator as I set up the account. What am I missing here?

Thanks!