First of all, is mIRC for you?
Yes, I would like to think it is. mIRC is a completely free, scriptable chat client that can connect to any irc server in the world.
Quoted from www.mirc.com

So if you have a windows computer, are interested in talking to people from all over the world, and especially if you would like to learn a new scripting language, mIRC is for you

Ok, so now that you've decided that you want mIRC, you need to get it. To download it, go to www.mirc.com and click 'Download mIRC' in the left nav bar. Now you are at a page with multiple options of where to download. All downloads are essentially the same thing, but I like to download from the host that is closest to me.

Alright, now that you have mIRC downloaded, lets get around to installing it. Navigate to wherever you downloaded the program to, or just find mirc62.exe (replacing 62 with the current version, currently the version is 6.2). Double click to run it. The install wizard is pretty self explainatory. At the first window, click next [img=http://img187.imageshack.us/img187/2298/1tg7.th.png]
then (after reading the ToS) click I Agree.[img=http://img303.imageshack.us/img303/6795/2ei1.th.png]
On the next screen, if this is your first install of mIRC, leave everything as-is, or the Full Install.[img=http://img257.imageshack.us/img257/1244/3zp7.th.png]
Click next. On this screen, youll need to specify where you would like to install mIRC to. Personally, I like it in my own section of the computer (C:/documents and settings/yourname/) however it defaults to C:/program files/mirc. Finally, select where you would like the start menu items to be installed, and click Install.

Now that mIRC is installed, open it up!
Once you get it open, the first thing youll see is going to be a little evaluation box. This can get quite annoying (especially after the '30 day trial' is up. Don't worry though, its free forever, and registering only gets rid of that popup)

After you get through that, the first thing you see will be something like this.
[img=http://img264.imageshack.us/img264/2915/4kj0.th.png]
You don't need to do anything special with that, everything there is sort of, optional but I'll explain each thing.

Full Name: Required, but it's ok to BS it, I change mine weekly
Email Address: Also required, but again, BS is ok
Nickname: This will be your displayed name, try to think of something unique because if someone else has it, you wont be able to use it.
Alternative: This is what you will default to if someone else is using your other nickname.

Nothing else really needs bothered with, except your server. First of all, there are tons and tons of servers.
The server that you can catch me on most of the time is irc.swiftirc.net although there are a bunch of others. I would recommend SwiftIRC for any beginners, because of its small size and also because im there.

Ok, so lets get you connected. You should still see a button that says Connect To Server, and beside that a button that looks like a flower. Click on the flower and you'll see this [img=http://img171.imageshack.us/img171/404/5sv0.th.png]
Where it says IRC Network: All, click the arrow. Browse through that list, and if you see something you like, click it, then click Connect To Server. If you dont see anything that you like, Click the 'Add' Button.

If You clicked the 'Add' Button, this section is for you, otherwise, skip to the next part.
[img=http://img324.imageshack.us/img324/403/6kj8.th.png]
Now I know there looks like alot of confusing stuff there, but trust me it's not to bad. First is the description, it can really be anything you want it to be, but i use the network name (such as SwiftIRC for irc.swiftirc.net) The IRC Server is the important part. If you couldnt find anything you were interested in before, try irc.swiftirc.net The port should stay the same (6667) and group and password mean nothing to you Finally, click 'Add' and then click Connect To Server in the next window.

Ok, now that you are all back to me, and everyone is connected to a server, lets get you into a channel. The easiest way is to think of one word that describes your interests, then prefix it with a # (that is the usual symbol to designate a channel) Now type /join #word (for instance, /join #music) On some smaller networks, there are alot of open channels, so you would be better to type /list this will give you a full list of all the channels that people have in them, as well as their topics and the number of people inside.

If you hadn't noticed yet, mIRC commands tend to start with / The / symbol makes mIRC recognize that youre trying to do something, and therefore doesn't send the text to the server.

Now that your'e in a channel, try talking. Yes, it's easy, just type your text into the editbox at the bottom of the channel window, and press enter. Now's when the fun starts. Try typing /me dances and pressing enter.

Also try using ctrl+k with your text (allows you to add color) as well as ctrl+b (bold) and ctrl+r (reverse text, or black bg with white text)