When you switch domain names to a new server it is often useful to make sure that the new server is ready for the domain before you do DNS updates.
Normally when you go to a webpage your computer will lookup the IP address of a domain name from your internet providers (ISP) name servers.
You can override this by fixing the IP address for a specific domain in what is called your local "hosts" file. As ever depending if you are on a MAC or a PC there are different ways of doing this.
PC: http://www.howtogeek.com/howto/27350/beginner-geek-how-to-edit-your-hosts-file/
MAC: http://www.makeuseof.com/tag/how-to-edit-the-mac-os-x-hosts-file-and-why-you-might-want-to/
REMEMBER: Whenever you've finished your testing to remove hosts entries that added for your testing otherwise you may not be looking at the correct server for a URL.