The machine will attempt to contact whatever DNS server is listed in it's network properties first. In the case of your domain controller, it will look to itself to see what domains it's authoritative for, and for everything else, it will use root hints to query additional domain controllers on the internet to determine the answer.
When you put in a forwarder, you typically do so, for either
1). Everything else that you aren't authoritative for
2). A specific domain...for example. *.mycompanieswebsite.com.
So, in the event that you are trying to accomplish #2 above, if you attempted to resolve the name of server1.mycompanieswebsite.com...your DNS server would try to answer it itself if it can (if it's authoritative for the zone) and if not, it will then send the query to the DNS server you have listed as the forwarder for *.mycompanieswebsite.com.
Hope that helps.