There are dozen clients but non as good as Hexchat (https://hexchat.github.io/downloads.html).
Download the for your system suitable file and install it:
Start HexChat.exe and wait for the window to show up.
Incase of HexChat being launched for the first time you will end up seeing the Network List.
In this example we will connect to the Kronos IRC channel which is hosted on the Mibbit network.
Obtaining the connection informations can be a bit annoying for some IRC networks however most of the time you do good hitting google with "XXX connection guide" (XXX is Mibbit in this case):
Now we can proceed adding the connection details in HexChat:
Go to the Network List window
Click Add and change "New Network" to a more fitting name like "Mibbit - Kronos"
Highlight the new network by clicking on it and hit Edit
The server format is domain/port
If we are using SSL we put a + infront of the port:
The Connect Commands offers the possibility to specify commands which will be executed after connecting to the server. Many IRC networks got a registration system in place where you register and auth with a bot user named NickServ. Using this tab you can for example auth yourself everytime you connect to the network.
A little explanation on how to register a nickname on mibbit can be found here.
After setting everything up HexChat should connect properly:
Staying in IRC even after closing HexChat
IRC cant be compared to messengers like Skype where you can for example send messages to someone being offline. You hold your nickname as long as you are online. As soon as you disconnect the nickname will be free again for use and someone else can connect under that name.
To avoid that someone else use your nickname you can register it. Depending on the network the person connecting with your registered nickname will be force renamed or will keep the name until you auth with your nickname.
Also there are bouncers. Those are programs running on a server keeping your nickname connected to the network 24/7. Imagine a bouncer as a proxy. You give HexChat the details of your bnc and it will connect through it to the network.
IRC looks complicated to those who never used it before and one may ask why we use such a system incase of Skype but once you made your first steps you will love it.
As someone who is interested in WoW development I can easily stay in touch with all projects I am interested in without adding thousand of contacts to some messenger: