So, you want to setup a LAMP-Environment at home? Quite easy, read a lot of Docs concerning apache and php-security for public accessible servers. Install apache, mysql, php and then setup a document-root-path where you have to install a standard-blog-software like loudblog…
With windows it’s just getting wampserver, installing it and then installing loudblog there.
Of course you need a static IP. Register a domain for that Ip.