CentOS Live Server Migration?

Hello, everyone. I've been lurking on this forum for a while but have never needed to post asking for a bit of help until now.

Long story short, I have a test of sorts scheduled with a prospective employer, a managed web hosting company, that involves migrating a hypothetical customer from their old server to their new server, hosted with the prospective employer. I have worked with Linux for a few years now, including at two unmanaged hosting companies for about three years, so I can handle the basics and a bit of intermediate stuff without any issue.

Unfortunately, due to my past jobs offering unmanaged hosting, we would never in a million years do something like this for a customer, so I am not familiar with how to do this. I know how to move data, users, and so forth over, basically via what is mentioned here, which we also would never do, due to learning on my own time. However, the stipulation that services on the origin server not be shut down during the migration process, which entails moving services over as well, has me scratching my head, hence my request for help or a few pointers regarding live services migration.

What I know about the impending test is that it "is a standard configuration not designed to be tricky." This is for web hosting, so I assume it will have Apache, MySQL, PHP, a mail server, and other basic web hosting services running. As far as the distro, it is either going to be CentOS, which I am most familiar with, or Gentoo. The person I was e-mailing could not remember which distro it was.

Any and all assistance regarding live server migration will be greatly appreciated, because how I perform on this test will likely determine if I remain laid off in Dallas or employed in New York City.

Are these virtualized servers?

I would start by finding out more about the data that you will be moving. Like What type of application this customer runs. when are they not getting hits. If they are always getting writes to the database then what time of day is slowest for them. Also if this is a heavily used web app expecting no downtime is quite a feat to ask for. But to move the database my suggestion would be to backup the database, restore it on the other server and then setup replication.

then I would point them to the new database so that all new writes will go to the new database while they are getting in between writes poplulated from the old db server.

course this is assuming that they are using
php , mysql , and apache like you said.