1. Get an IRC client. For most of you this will probably entail looking for an IRC program icon and clicking on it :). If you do not have one, I recommend mIRC (for 16 or 32 bit Windows). To go to the mIRC homepage, click here. A good MacOS IRC program is ircle (so I have heard), and for Unix: try BitchX. If you have a different OS, you can probably find a good IRC client for it at tucows.
2. Learn how to use it. Ok, easier said than done. Try reading the help files that came with your client. There is also a good newbie turorial here (in the Newbie Area), and a newbie FAQ here. To get a comprehensive list of IRC commands, click here or here. You can probably skip most of this step for now by following the next few steps closely.
3. Set up your nickname and user info. This should pop up (in mIRC) as soon as you start it, and you can reach this screen with alt+E. Chose a nick and an alternate, your email address, and I recommend just your initials or nick for "real name" since anyone can see this info. Here is an example of mine:

4. Add the FEFnet server. You may already have this in your server list, but if not, click the [ADD] button on the screen you typed your nick, full-name, & email address on (above). You should get a box that looks like this:

5. If all goes well, you should connect to an FEFnet server, getting the 'Message of the Day' from that server. If you get an error like "No IDENTD installed" or "Server full" then try again. irc.fef.net is not a server but a random link to all the FEFnet servers, and some will allow different people to connect, at different times (note, if you don't get a -irc.fef.net- *** Looking up your hostname... type message before "unable to connect" then repeated tries might not work, as you may have some other IRC client or ISP problems). Once you get on a server, a channel folder should pop up. Type in #lexx here and click [Join]:

IF all goes well, you should end up in the FEFnet #lexx backup chat room.
<Splarka> Welcome to IRC. <DDC> IRC? <lefty> We're in IRC? * Splarka nods. <DDC> So, what are we supposed to do now? <Splarka> Perhaps you should find yourselves a channel. <lefty> But IRC is full of depravity and evilness, and darkness and- <Splarka> My old friends came from IRC. <Splarka> I was taught that although there are not many good channels, there are some. <Splarka> Perhaps you should find one. <DDC> You mean, we should find one, were together in this. <Splarka> I'm idle, I have no future.