First, when configuring third-party DNS, make sure that you have configured the names that you will be using for your site as aliases on the Site Information page. Otherwise, when the request gets to our network, our servers will have no idea what site you want and will return an "Unknown Site" error message.
The preferred way to set up third-party DNS is to create a CNAME record. This allows you to take full advantage of our load balancing and fault tolerance features to get the best performance and reliability for your site. If your site was named example and you wanted to use the domain name www.example.com then you would configure a CNAME record from www.example.com to example.nfshost.com.
However, you cannot use a CNAME record with a bare domain name (such as example.com without www. in front). All domain names have special records, called SOA records, which must exist. But CNAMEs must not coexist with any other records. So, if you attempt to point example.com to example.nfshost.com via a CNAME record, you will violate the DNS specification because the mandatory SOA record won't be there. This will cause all kinds of unpredictable and hard-to-diagnose problems with your domain.
In such cases (or if you just hate CNAME records) you can also use A and AAAA records with the IP address(es) for your site to set up third party DNS. They're at the bottom of the Site Information panel in the "Web Site Addresses" box.
The caveat with using A/AAAA records with third-party DNS is that you are then responsible to keep them up to date if they change. Fortunately, that's exceedingly rare, and in most cases the old IP will continue to work for several months. As long as you make a practice of checking on it from time to time (set a reminder!), it will typically be fine.
The major exception to "typically" relates to DDOS attacks. If there is a DDOS attack on a specific IP address, we may have to disable that IP address without warning and move affected sites to another one. If you're using our DNS, that's no problem. If you're using third-party DNS with CNAMEs, that's no problem. But if you're using third-party DNS and you're using manually-configured A records and the IP address you're using gets attacked and we have to block that IP to mitigate the attack, then you may experience downtime until you manually update your third-party DNS. Such circumstances are rare, but they do happen.