The most important thing to tackle this problem is preparation. We should be always preparing for it. The main part of preparation is we should be always taken care about server fail ours. If any problem occurs in it, we should contact to customer support team very quickly.
Check for site working properly or not
Whenever you switch your site from one server to another it will take approx 24 to 72 hours to properly move. So you shouldn’t cancel the old hosting at 72 hours. You should wait for visitors are looking your site or not. If once visitors are coming on the website and you don’t get any error pages, think your site working properly.
Backup Your Files
Whenever you are switching your website from one server to another, copy the files in the same place on another server. If your website contains SSH and Rsync then the backup of your server data will become easy. By the help of control panel facility, you can easily zip your file in your public HTML directory. You can download these zip files later in your new host. You can make your database backup by the help of control panel, phpMyAdmin, command line etc.
Now Upload Your Files on new server
After switching off your website on the new server you can upload your files, data and all the necessary thing of your website on the new server.
Ensure that everything is working or not
At last, ensure that everything is working properly or not. And if there is any issue then you can contact to customer support team. They will resolve your problem.