Hi,

I want to transfer my domain, to the cpwebhosting, and will go with the linux shared hosting account.

You need to just change the Domain Name Servers (DNS) setting with your current domain registrar.
You will get the mail which states that:

You have chosen to transfer domain “domain-name”. To complete the transfer, you need to contact your Domain registrar and have the DNS information changed; otherwise your site will never be available online.

There must be a transition plan to minimize your site downtime. Changing your DNS settings to point to your new host has a propagation period. I suggest you transfer your files first and once this is complete, that’s the time you change your DNS settings.

That is correct, your new hosting company will provide you with the needed information and you will then have to have it changed in the registrar system so that your domain points to the proper location.