Transfer a WordPress site from one server to other during high traffic time is a quite difficult task. But you can transfer a WordPress site with zero downtime with simple technique. A WordPress site consists of two key parts i.e root file system (your wordpress installation) and MySQL database.
Technique to transfer a WordPress site
First step is you need to backup the wordpress site. You can use plugins like Backup Buddy, Back WP Up, Online Backup for WordPress plugins. You need to take backup of both file system and database. After taking backup, you need to download and extract the zip file. You will need a FTP tool to upload the backup to new server. After that login into your control Panel of the new server. Go to the MySQL section and create a new database and save the user information.
Open wp-config.php file in the backup you have downloaded and update the database name, user id, password and host name. Usually host name varies with the hosting service provider of yours. ( For Hostgator, it is localhost . Please contact you Hosting provider for host name of the database.) Using FTP clients like Filezilla, login into your new server and upload the file system folder to new server. Open the MySQL admin in your control Panel of the new server and select the new database you have created. Select the import tab and upload the backup database.
The shifting has been completed. Now you need to change the dns to new servers. Within 5-10 minutes, your site will be redirected to new server. Use Google Public DNS in your PC to see the DNS changes faster.