You need a supported deskphone, and the 3CX Windows or 3CX Webclient working in CTI/CSTA mode.
Then you simply dial in the app and the deskphone makes the call
If you have one to test, we can tell you how to switch to CTI or CSTA mode.
As for the clipboard there is no special support, you either paste the number into the 3CX client or you find software that will do the dialling for you.