You can test a WordPress site (before editing live dns) by editing your local hosts file using the server IP.
This process ( a common developers method and is required for any web host, not specific to us) is the only way to pre-test a wordpress site. Editing your local hosts file tells your web browser the IP to lookup specific domains, before it looks them up on the global dns system on the internet.
So it's tricking your machine and just your machine into thinking
targetdomain.com is at IP 123.456.789.123 - but for everyone else it
will stay pointing to the other live IP (old site).
So, to edit your lcoal hosts file, it's just a couple of lines in a text file. The process varies from OS to OS (windows/mac) you can google 'how to edit hosts file for... ' add your OS etc.
The lines you'd add would typically be in the format (note you'd replace IP number with the target server IP):
123.456.789.123 www.targetdomain.com
123.456.789.123 http://www.targetdomain.com
123.456.789.123 http://www.targetdomain.com
(exactly as they appear above)
Once you've added these to the hosts file on your computer, save it, then refresh your browser, maybe need to restart and then visit: www.targetdomain.com
You'll see the new site and be able to navigate and login to wp as if it really was live on that domain. But this is only affecting your computer, no-one else, until the dns is updated with the new IP.
When you finish testing, remove the lines from your hosts file.