Migrating a website to new hosting without downtime involves backing up files/databases, setting up the site on the new server, testing via a hosts file modification, and finally updating DNS records. The key to zero downtime is keeping the old site active until DNS propagation completes, usually within 24-48 hours. 

Step-by-Step Migration Process

1. Prepare and Backup: Perform a full backup of all website files, databases, and SSL certificates from the current host. Perform backups on your hosting server, and if you are using WordPress, also make a WPress backup. 

2. Lower DNS TTL: Reduce the Time to Live (TTL) on your DNS records to the lowest possible setting (e.g., 300 seconds) a few days before the move to ensure faster propagation.

3. Set Up New Hosting: Purchase the new hosting plan and create a new database/user. Upload the website files and import the database to the new server.

4. Test via Hosts File: Configure your computer's hosts file to map your domain name directly to the new server's IP address. This allows you to verify the site works perfectly on the new server without affecting live traffic.

5. Update DNS Records: Once testing is successful, change the Domain Name System (DNS) settings to point to the new server's IP address (A record) or update nameservers.

6. Finalize Transfer: Keep the old host active during the propagation period (up to 72 hours).

7. Remove Temporary Changes: Remove the entry from your hosts file and, if necessary, re-sync any data (like new comments or orders) that occurred during the switch. 

Key Tips for Zero Downtime

• Do Not Cancel Old Hosting: Keep the old account active for at least 48 hours to ensure all users see the new site.

• Use Migration Plugins: For CMS platforms like WordPress, tools such as All-in-One WP Migration simplify file and database transfers.

• Freeze Content: Avoid publishing new posts or changing content on the old site during the migration.