The first thing that one needs to do before they can use IRC is to download an IRC client.  I think the best one (out of the three that I have tried) is mIRC.  The following are instructions of installation, setup, and basic usage of mIRC.

1.) Download mIRC  (This link will open a new window.  When download is complete, you can return here and resume.)

2)  Installation/setup
To install mIRC, just run the mirc.exe and follow the simple instructions.

3) Configuration
First launch the mIRC program.  After closing the 'greeting' box, goto File > Options in the pull down menu.  (This box might show up automatically.)  The pop-up should look something like this:

Type in your personal information -- Full Name (no, it doesn't have to be a "real" name); e-mail address, Nickname that you wish to go by, and also pick an alternative nick just in case your first choice is taken.  Next you need to fill out the server information so that you can connect to the right network.  Since the server that the #Nosgoth chat is on is a relatively smaller and less known server, it most likely will not be already listed.  Hit the "add" button:

Fill in the information just as the image above shows.  Description: Espernet; IRC Server: dream.esper.net; and Port(s): 5555.  Everything else should be left blank.  Hit the OK button after filling in the information.  Now select the "Connect to Server" button.  If it connected correctly, then you normally will see a rather long "greeting" message in the status window.  Once connected, the channel folder should appear.  Type in #Nosgoth into the box, hit add, then join.

[Note:  If the folder did not show up, you can select the third icon underneath the pull down menu]  Another way to join the channel is to type /join #nosgoth in the status window.  If successful, another window will pop up with "#Nosgoth" as it's title.  And you're there.

As you can see, stumbling into a chat in-progress can be confusing at first.  (Realistically, you would most likely have been greeted upon entering though.)  To add something to the conversation, just type something in the area below the conversation and hit return.

     NickServ

[Note: wherever the text is italicized (like this)  is where you would substitute something else for the command.  If a command that says /msg NickServ identify password instead of typing "password" you would type in your password.]
 

Register Nick  If you have a name that you always go by and are known by, such as at the forum, then it is a good idea to register your nick.  NickServ allows users to 'register' a nick, stopping others from using that nick (if they hadn't registered it themselves first), and even allows the owner of a registered nick to disconnect someone trying to use their nick.  (If a registered nick is not used for 30 days, then it will be 'dropped' and can be registered again by another user.)  To register a nick, first make sure that you are already using the name you want to use.  (It will be listed in the title of the Status window.)

   /msg NickServ register password

Don't forget your password!  If you do it is a hassle to get it retrieved.
 

Identify Nick  Sometimes, in order to be recognized as the owner of your nick (you must have registered it) you might be asked to "prove" it.  This is especially true if you set the "kill" command.

   /msg NickServ identify password
 

The KILL command  After registering your nick, if you are very protective of your name and you want to make sure that no one else uses it, then you can set the "kill" command.

   /msg NickServ set KILL ON  (To disable, type /msg NickServ set KILL OFF)

When someone on that server (Espernet, in this case) connects using the name in question, even you, NickServ will prompt the user to identify the nick or they will be disconnected from the server in 60 seconds.  So if you decide to use this, then make sure that you are quick enough to type in the identify command...
 

Recover and Release  I've noticed that sometimes even if you set the Kill command it may not work (especially if they are using the same comp that you registered your nick on).  So if you happen to catch someone else using your registered name, you can kick them off.  (Although, you should be "courtious" and ask them to change to a different nick first and if they don't then use force.)

   /msg NickServ recover nickname password

When you give this command, NickServ will bring a fake user online with the same nickname as the user you're trying to recover your nick from.  This causes the IRC servers to disconnect the other user.  This fake user will remain online for one minute to ensure that the other user does not immediately reconnect; after that minute, you can reclaim your nick.  Or, you can just use the release command to get it back sooner:

   /msg NickServ release nickname password

You should then use the identify command to make sure that you are accepted as the registered user.
 

   Various other tricks and commands:

Actions  To do an action that explains what you are doing, or what you wish you could be doing, you would type:
   /me whatever the action is

For example if you are "C00l_DuDe" and you type /me drops a boulder on Galvatron's head then you would see:
* C00l_DuDe drops a boulder on Galvatron's head
 

Sending a private message  If there's something you want to say to a particular person in the chat but don't want everyone else to read it, then you can send them a private message.

   /msg name (of person to send msg to)  message

Let's say that Akira hadn't relplied for awhile and I wanted to check up on him without bothering everyone else, I would type /msg Akira Is your computer still giving you problems?  Akira would get a seperate 'chat' box pop up with my name at the top and would see: <CyborReaver> Is your computer still giving you problems?  [Note: using /query name message does the same thing, but opens a new query box on your side as well even if the person does not reply.]
 

Channel Information  If you want to know the 'boring' information about the channel such as when it was created, when it was last opped in, what the last topic was, the description, etc. then you can request info on it from ChanServ:

   /msg ChanServ INFO #Nosgoth
 

Access Levels  There are different access levels that a user may have in a channel.  The levels, from highest to lowest, are Founder, SuperOp, AutoOp, and Basic.  (Most users are Basic, while CyborReaver is the one and only Founder.)  Still, if you are interested in checking on your access level, you can do this:

   /msg ChanServ ACCESS #Nosgoth your_nick
 

MemoServ  This is a utility which lets registered users send memos to each other.  (Like a mini e-mail service within IRC.)  A user need not be on line at the time a message is sent.  Here's the basics (more info can be found by typing /msg MemoServ HELP.):
 

   /msg MemoServ LIST   Lists the memos you have recieved in a numbered order.

   /msg MemoServ READ {number | last | new}   You can read a message by giving its number, or just read the newest by typing new.  Last reads the last message recieved.

   /msg MemoServ DEL {number | all}   Deletes a numbered memo, or deletes all your memos.

   /msg MemoSev SEND nick memo-text   Sends the named nick a memo including the memo-text.  You can also send a memo to a channel.  (To send a memo to #Nosgoth, replace the nick part with #Nosgoth.)