Most probably think it's easy, but at first I was a bit confused on how to chat. So I have written this small howto. Hope it's useful ;-)
If anything is missing or inaccurate, please tell me.

Using the built-in chat applet

1) Go to the following page :
http://www.longplays.org/irc.php

2) Enter a nickname. Choose the same that you have used to register on the website, it'll make it easier to figure out who's who.

3) A chat room appears. On the right is a list of connected users. When you type in a message, it appears in the main window, and all connected users can see it. Their answers will appear too.

4) To have a private chat with someone, click on his name and choose PM. A separate tab will open. The messages you both type in this tab can only be seen by you two.

5) When new messages are typed in by someone else (either the main chatroom or private chats), the tab title turns blue.

Using standalone irc client

1) Download and install mIRC. Get it here:
http://www.mirc.com/get.html

2) Each time you start mIRC, it warns you about an evaluation period and asks you to register. If you use mIRC on a regular basis, then you should consider doing so, but otherwise, just click Continue. The program remains fully functional.

3) In the Options dialog box, select the Connect section. Choose a nickname and an alternate one (in case someone is already using you nick, or in case you're already connected somewhere else, for instance). Select the Connect / Servers section. Click on Add. Choose a description ("Longplays", for instance). In the IRC Server field, type in "irc.abime.net" (without the quotes). Click OK. This is a one-time procedure.

4) Connect to your new server. The Channel selection dialog box should appear. Type in "#longplays" (without the quotes) and click Join.

Note
Admins and regulars are generally connected at night, Central European Time. They're here to help you with recording and encoding issues.