subdomain points to development server issue

My client has an existing web site. I have purchased new hosting for a new site under development and installed WordPress there using their domain as a reference.

The domain is registered with a 3rd party. We created a subdomain (http://newsite.discovereuropeltd.com/) to point to the new WordPress install. Now I can see the site in a browser (though it seems to lack any sort of formatting) but all the links go to the main domain, and my login attempts fail. It tries to transfer to a WordPress dashboard at:

http://discovereuropeltd.com/

NOT

http://newsite.discovereuropeltd.com

I guess I might re-install using the subdomain, but how would I control the changeover to the main domain when the new site is ready to go live?

Is there a file I can modify to correct this? Was there a better way to do this?

Thanks in advance for any help,

Max