The answer will differ depending on whether your local network is on a dedicated IP or not.
If your external IP is dedicated, set an A Record to that IP. You should be able to do this through your domain provider's control panel.
If your external IP is dynamic, like on most home networks, you'll need to use a Dyamic DNS service to always update your domain to point to your local IP, even after it changes. Dyn has been doing this for as long as I can remember, but plenty of organisations offer this service.
After that, it's down to your local network config, which hasn't been mentioned in the question. Presuming you're behind some sort of router, you'll need to tell that direct traffic to your local server's local IP for whatever ports you're using.