How to Connect a Third-Party Domain to a Shopify Store

1. Navigate to the general Settings 
2. Go to the Domains section
3. Click on the Connect existing domain button
4. Enter your domain name
5. Click Next and Verify connection
6. After that Shopify will provide you with DNS data for 3 records: A, CNAME, TXT
7. Go to your domain provider, add the DNS records
8. Come back to Shopify, and click on the Verify connection button again
9. Wait at least 48 hours until everything gets synchronized and starts working

Read also "How to Buy and Connect a Domain on Shopify" and "How to Change myshopify.com Subdomain"