First of all,
Set Up Your Hostname
Most internet home users do not have a static (fixed) IP address on their ISP subscription. With dynamic IP address we need to use dynamic DNS service such as www.noip.com to point at our hostname correctly every time the IP address changes. This can be done by using a client application (here) or a build-in client inside a router.
Free DDNS service : using a subdomain with limited choices
Plus Managed DNS service : $24.95/year using your own domain name
View noip.com package here
Set Up Your Network
Check your home computer IP address using ipconfig at command prompt. Open your router configuration to assign port-forwarding on port 80 to your home computer IP address at port 80 also. This will establish a direction connection between the home computer and the internet by its hostname.
Set Up Your Application Server
The most simple installation would be using www.instantwp.com and ‘voila’. Now you are ready to do blogging or extend your wordpress to become web application for e-commerce, forum, video streaming, auction, job listing, rental or any site which suits for your needs.
Otherwise you can do this the conventional way :
– install apache web server
– install PHP 5+
– install MySQL or MariaDB
– install WordPress
Good luck and be happy