I have a dedicated working server at home (LAMP and localhost). I also have a domain name.
My questions is, given my domain name, how can I make that public
.com site point to my home computer?
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Get your ip address by googling "what is my ip address". Then take that ip address and add an A record for your domain that points to that ip.
If the computer that's hosting the site connects to the internet through a router then you will need to log into the admin gateway for that router by typing your default gateway ip address into the address bar in any browser.
Your router's ip will usually be 192.168.1.1 or 10.0.0.1.
Once you log into the admin portal for router then you will have to forward ports 80 and 443 to the internal ip of the computer that is hosting the site.
You can get the internal ip of your computer by typing either
ipconfig into your console or command prompt. Your internal ip will usually start with 192.168.###.### or 10.0.###.###.
First know your web server's ip address. After that edit your domain's A record and point your domain to that ip. You do this by adding an A record for @ points to your ip. You also need to port forward your router so that your web server can be accessible from other computer on internet. For detail walkthrough read this article on pointing domain name to home web server.