Do you want a test subdomain that others can see, or do you want to see the actual final domain on your own machine?
For the former, the subdomain stuff that others suggested will do the trick. But if you just want to see your new site on your own machine, there is an easier way to do it. Edit the HOSTS file on your local machine and add an entry for your domain pointing to your new IP address on DreamHost. Then you will see your site at its actual domain instead of a temporary subdomain.
On recent versions of Windows, the HOSTS file is in the system32/drivers/etc subdirectory inside your Windows directory. On other systems it will be in other places. It’s a good file to get familiar with.