transfer a website in coldfusion technology

BrainSee wrote: Can I simply copy the files in the main directory of the server to past them in the other server

Maybe, but unlikely.  First of all the second sever MUST also be a ColdFusion server.  I.E. it must have some version of a licensed (if you want other people to access the site) ColdFusion Application Server OR one of the other CFML engines.

BrainSee wrote: there is a databse to save?

Most likely.  While ColdFusion COULD do a lot of dynamic site building without ever touching a database.  Interacting with database is the heart and soul of CFML and most people would have used at least one in their web application.

BrainSee wrote: What the way to save the database, and how to reinstall the website in the other server?

What to do about the database depends entirely on what database was used.  But they all have some way to migrate data.  You will also want to be concerned about settings configured in the ColdFusion administrator.  Things, such as the Data Source Name, which has all the connection information to the database.  ColdFusion provides CAR (ColdFusion Archive) functionality to export and import settings.  But one needs access the the ColdFusion administrator to do this.  And the ColdFusion needs to be an Enterprise OR Development licensed version.

Finally, the CFML code used in the web site may NOT all be in the web root.  There are ways to use reusable code such as Custom Tags and Components that may be located in other locations in the file system to which the ColdFusion server has access.

Really if you know NOTHING about ColdFusion, you probably really should contract with somebody who does to do this for you.  Otherwise you had better be willing to crash learn about it and schedule yourself plenty of time for trial and error to accomplish this.