There are numerous web clients that can be used to access IRC.Note that these are usually made for Unix-like operating systems such as Linux and OS X. These are often found on the website of the organization that has an IRC room or channel.
HexChat is the successor to the most popular Linux client for IRC XChat.These will usually limit you to access to a particular channel or network. It can probably be found in the software repository of your Linux distribution of choice, if not preinstalled. Unlike XChat before it, HexChat is completely open source software and free of charge on all platforms.