moving the site to a different folder

Hi there, I would like to move my site from carlacuomo.com to carlacuomo.com/blog and then install a new theme on carlacuomo.com so that I can keep my old site and then just work on a new theme as at the moment I am still on Kubrick default. I know that this process should be done via ftp ( I use fizella) but I am not too sure where to create new directories ( .com and /blog ) and where to point the material

if anyone of you have done this before I would be very glad to know the right procedure
thanks