I thank Jenny (carrotbat) for these instructions and screen caps ...
First, go to http://www.ircle.com/download.shtml
and download the appropriate version of Ircle for your OS. These screenshots were taked on Ircle 3.1.2, Mac OS X 10.4.4, but Ircle functions pretty much the same no matter which version you're using.
The Ircle icon will probably look something like this:
Open Ircle. If it's the first time you've opened it, you'll see a license agreement for the trial; if it's after that you'll see a screen asking you to pay up; and if you've paid, it won't show anything at all. Click "I agree", "Not Yet", or sit tight, depending on which is the case. (The trial is for 30 days; after those 30 days are up, you can still use it, but it'll disconnect you ever half hour. Either put up with that, find a way around it, or pay.)
When Ircle is finished opening, you'll get a collection of small windows, which will probably look something like this, only more spread out: click to see larger picture
(If you don't see all these windows, you can open them via the "Windows" menu.)
In the connections window, make sure the first connection is highlighted (as it is in the picture), then click the "Edit..." button. The Connection Preferences window will appear.
Pick a nickname and type it in the "Nickname" field. You can also enter information into the "Username" and "Real Name" fields, or leave them at the default; it doesn't matter.
As it happens, the default server here is the correct one, irc.undernet.org , but if it isn't, click the "Select" button next to the server name. A list of servers will pop up.
These aren't anywhere near all the IRC servers available, but they're enough for our purposes. Pick an Undernet server (labelled as such in the 'Network' column), and click "Select".
You'll be returned to the Connection Preferences window.
Everyone who didn't need to pick a server can start paying attention again here.
Click the "Okay" button in the Connection Preferences window. It will close.
Now click the "Connect" button in the Connections window.
(If you've read Zoomway's mIRC tutorial, know that Ircle handles duplicate nicknames slightly differently: it'll pop up a window asking you to enter a new nickname if yours is already taken.)
It may take a few seconds to connect (or a few tries -- undernet servers can be busy), but eventually you'll see a bunch of messages scroll by, and the icon next to the server name (in the ever-popular Connections window) will change from a broken pipe to a double arrow. click to see larger picture
In the inputline, type "/join #lanekent", followed by a space and the password if necessary, and hit return. click to see larger picture
And there you are!