How to Move Site?

So, I have an old website at: http://www.migueldemaria.com/

I have made a new website here at: http://www.migueldemaria.com/blog/

I want to move the new website to the old address, that is, I am ready to get rid of the old content and use the new stuff. I want to make sure I use best practices and don’t mess things up! In a nutshell, could someone tell me the basic things I need to do? I can follow the tutorials, but would like a big picture overview. Thank you!