Using mIRC, xchat, AmIRC or something similar to use the chatroom might be easier, especially if you have an older computer.
If you use Windows:
mIRC for Windows can be found on http://www.mirc.com/
As an alternative, you can use PIRCH, which can be found here. I cannot guarantee that these do not contain any spyware etc.
If you use Windows, OS/2, Linux, *BSD etc.:
You can use xchat, which you can find
here. xchat might require a more powerful computer than mIRC or PIRCH.
Also, Mozilla (not Firefox) comes with an IRC-client, which you can find on the small button-bar on the left bottom of the Mozilla-window. It's called Chatzilla.
Install the program in the normal way. Then, start it.
Many of these programs contains a list of IRC-servers, and gives you the possibility of entering your nickname. Doing the latter might be a good idea.
You can also add the details for the chatroom to the list, or you can connect directly - I'll show you how, in a minute.
Here are the details, for those who are interested:
Server: irc.freenode.net port: 6667
Channel: #wrongplanet
If you decide to connect "directly", ie. without adding things to the list in your IRC-client, here's how to do it:
Get a text-window (in the IRC-client). This can often be accomplished by connecting to any server. When you have the text-window in front of you, type:
/server irc.freenode.net:6667
Some time will pass. Hopefully, you will be connected.
Did you set your nickname? If you didn't, now might be a good time to do so. This can be accomplished by typing:
/nick YourNickHere
In my case, I would type "/nick Minus".
Finally, join the #wrongplanet-channel. You do this by typing
/join #wrongplanet
And you should be in. A new window pops up, with a list of the others that are there. Hopefully, there will be something happening in the chatroom.
Hope this helps. Let me know if you have any questions.