Site Daemon
This is very easy assuming your current site is running under cPanel.
Ok for example you want to transfer from ARVIXE shared hosting to GoDaddy VPS or vice versa, just make your new server is a VPS so that you will have a WHM/cPANEL access. Login to your new server WHM usually this can be access from this url https://YOURNEWSERVERIP:2087 then follow the screenshot below :

Once done point your domain name server to the your new ip address for example :
ns1.yourdomain.com it should have the ip address from the new server
ns2.yourdomain.com it should have the ip address from the new server
if your domain name is hosted in godaddy there is a section there to add host for your name server.