IRC is free to connect to and speak on. Channels are free to join too.
mIRC is a separate program that adds a graphical interface to IRC. mIRC is not the same as IRC. mIRC costs $20 USD to register, although the first 30 days is free. This is a one time registration and entitles you to use ALL future versions of mIRC at no extra cost.
Information on registering can be found here