Unless you've paid your ISP for a block of public addresses, you only have one (which may be dynamic - changeable). That address is assigned to your router which becomes the gateway to the outside world. You then port forward port 80 (I assume you're using) to the computer that is acting as a server. So it would look like this:
Router (public IP address) --> forward port 80 to Server (local IP address).
You will also need to make sure any firewall on the router and/or server allows inbound requests on port 80.
Finally, you need to make sure you've configured your registrars DNS servers, to point your domain name to your public IP address.
Note, it's unlikely you'll be able to access your website by simply using a browser on the internet. Why? Because you're on the wrong side of the network. The solution is to map the domain name to your local server IP address in your hosts file on the computer you are using to access the site. For example, if your server's IP address was 192.168.0.1, and your domain was example.co.uk, this is what it would look like:
You can check the site is active to the outside world, by using any one of the many public proxy servers in your web browser and enter your domain name.