DiscIRC is a bot that syncs messages between Discord and IRC. It's written in Python using the discord.py and bottom libraries.
You can install it simply using pip:
$ pip install discirc
You first need to configure DiscIRC thanks to a config file. By default DiscIRC tries to load a ~/.discirc file, if not present you need to give it to the app with the -- config option.
To create a valid config file please see the example.
Then simply run DiscIRC thanks to the available command:
$ discirc
DiscIRC handles private messages. You need to prefix your message with a @User when sent from Discord and with User: from IRC.