You're going to need to create a datasource on the destination server via the ColdFusion administrator. Upon setup, it will ask you for the DB credentials -- server name, user name, password, and DB name... there's also some advanced features there that you play with but for getting it up and running they are unimportant.
The key here: somewhere in the site's code, there's going to be reference to the datasource. Up until ColdFusion 9, this had to be provided with each statement. Do some digging through the sight and see if you can come up with this. When you find a CFQUERY, look for the "datasource" parameter to the tag.
Example:
<cfquery name="myQuery" datasource="myDatasource">
In this case, the datasource name would be "myDatasource" (no quotes). You'd probably want to use the same name for the datasource in this case, otherwise you'd have to go through all the code for the site and change it to whatever you have named the datasource on the new server to be.
Many developers, however, might set this as a variable in their application.cfc (or .cfm for older CF versions). In which case you might find something like this:
<cfquery name="myQuery" datasource="#application.datasource#">
In this example, the datasource name is being passed through as a variable, most likely from the application.cfc (or application.cfm) file. You'll need to track that down and find out what it is being set to. The good thing about this though, is that if you can find where that is set, you can easily change the datasource name to whatever you want without having to fish through the code.
Good luck in finishing up the move!