how to access the local server host website in the internet

The following should give you enough to search for discussions, as well as some general details of IP network gizmos and boxes: You'll need an ISP tier of service that allows remote access and preferably with a static IP address (static versus dynamic IP). This as various ISPs prohibit server-oriented protocols such as HTTP TCP port 80 traffic, and some firewall server-oriented ports. You'll then either need to use either dynamic DNS with your public dynamic IP — this is the hacking-around and not-really-for-production approach — or static IP with traditional DNS, and you'll also need to enable what's called port forwarding (sometimes also called virtual server) through your gateway-firewall-NAT device and into your server for TCP port 80 and possibly also TCP port 443. This port forwarding gets the incoming connections from the 'net into your public IP address (static or dynamic) mapped through to your NAT'd IP address space and your private IP address for your server.

As the first part of getting any of this to work with OS X Server, launch Terminal.app on the server and issue the following harmless diagnostic command:

sudo changeip -checkhostname

This checks for common errors in the local DNS setup, and broken networking and broken DNS tends to cause other errors elsewhere in the environment. You'll need to enter an administrative password for the sudo, you might get a one-time informational message from the sudo, and you'll then get some configuration details and then an indication that DNS and local networking needs no changes, or that there are configuration issues.