Looking to replace old wordpress site with new one

So there may be an answer to this already out there, but I haven’t found it yet. I have a current site at http://www.DontStayBroken.com. I’m rebuilding it using a new theme and some new plugins. What I did to do this was I used Installatron to clone the wordpress installation over to update.dontstaybroken.com and I’ve done all the rebuilding there. Now I’d like to replace the old site with the new one? How should I do that? Let me know if you have any resources that might help.