Here is some good resources :
http://codex.wordpress.org/Giving_WordPress_Its_Own_Directory
http://codex.wordpress.org/Changing_The_Site_URL
And here is another way of doing this :
First install the theme on your new website,
then go to your previous website and backup your site using wordpress export tool (tools > export)
back to your new website and import the ?export file? using wordpress import tool (tools > import)
screencast is also available (installing and importing data)