I am very new to webmastering as a volunteer for a non-profit. I had some help setting up an account with DreamHost. Because the organization for which I am webmastering already had a new domain name registered which we wanted to use but could not access at that time, we set up the DreamHost account with a temporary domain name XXXXXXX.org. The person helping installed a WordPress account which I have used to set up a temporary placeholder page to redirect viewers to our existing website on another host (with yet another URL YYY.com) which will eventually be replaced by the site on DreamHost.
Since then, I have got control of the domain name that we want to use ZZZZZ.org (not the one for the old website, YYY.com) and transferred it to DreamHost where it redirects to the first DreamHost domain name XXXXXXX.org.
What I want to do is switch the two domain names and make the ZZZZZ.org the "official" name for the website which shows up as the address in browsers. and redirect XXXXXXX.org to ZZZZ.org.
If you can help, please describe the process in great detail so that I can understand and follow the instructions. Thanks for your help.