The recommended method of testing websites before changing DNS for a domain is to edit the local hosts file on your computer. This will bypass the DNS lookup from your computer to that domain – allowing your computer to "see" the site as it is in your new service without making any changes to the site or the service.
This is the preferred method to test your site, as many sites (and most common site software such as WordPress) use Apache mod_rewrite rules – other methods of testing a site before changing DNS can interfere with the way these rules allow your site to work. This method is a bit in-depth and requires some working knowledge of your operating system. I will attempt to break it down as much as possible.
C:\windows\System32\Drivers\etc\hosts
C:\windows\hosts
127.0.0.1 localhost
127.0.0.1 localhost 67.222.1.2 example.com 67.222.1.2 www.example.com
ipconfig /flushdns
sudo nano /etc/hosts
127.0.0.1 localhost 67.222.1.2 example.com 67.222.1.2 www.example.com
sudo killall -HUP mDNSResponder
sudo discoveryutil udnsflushcaches
sudo killall -HUP mDNSResponder
dscacheutil -flushcache