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Make sure that the DNS server you use knows about your domain name. Typically, inside a local network, that means that you need to configure your DHCP server to use your own DNS server, and configure your DNS server with your domain name.

For this to work outside the local network you would have to register your domain name to make it official so any official DNS server can give the IP to your domain. This is the "real" way. The other methods here are ways to make it look like you have done this.

Also, you may need to configure your router to allow outside computers to access the servers inside your network.

Or just add your domain name to the hosts file on the computers you want to know about your domain name. This is much easier, but you need root access to the computers that you want to change the hosts file on. The hosts file is just a local translation list for domain names and IP. For this to work outside the local network you must have a static IP. Otherwise you need to use some dynamic DNS service.