To resolve a domain error in Shopify, first, verify your domain settings by logging into your Shopify admin panel. Navigate to "Online Store" and then "Domains" to check if your domain is correctly connected. Ensure that your DNS records are properly configured; specifically, the A record should point to Shopify's IP address, and the CNAME record should direct to "shops.myshopify.com." If you recently purchased or updated the domain, allow time for DNS propagation, which can take up to 48 hours. Lastly, if issues persist, consider reaching out to Shopify support for further assistance to ensure a seamless online presence.