If you have purchased NS1's Dedicated DNS product, your zones can be served by either NS1's Managed DNS Network, or your dedicated network, or both. You can easily configure which networks are serving your zones by following these steps.
Open the zone you wish to update and click on the Zone Settings tab. At the top you should see two checkboxes, one for the NS1 Managed DNS Network, and one for your Dedicated DNS Network. Check the boxes next to the networks on which you wish your zone to be visible, then click 'Save All Changes'. For a redundant setup, you'll want to make sure your zones are visible on both networks.
Now open the Nameservers tab and you will see the nameservers associated with your dedicated network. You’ll want to update the registrar settings for your domain to include all of the nameservers listed here.