theorganisedhousewife on "I don't understand web hosting"

hi, my blog appears to be going well with alot of interest. I would like to change and customise my blog theme and create facebook page links, but can't do this to a .wordpress.com site, so I have purchased a .com.au domain. What do I need to do now, do i need to change to wordpress.org?? Do I need to find a web hosting site?? I am really confused on where to go from here. If I do need to move to wordpress.org, can I take all my old posts over?
Really appreciate your help and direction.