The Basics: Basic IRC commands to get you started

/join
Type /join #channelname -- to join a channel of your choice
Example: /join #Lobby

/me
The /me is an action message.
Type /me 'does anything'
Example: /me waves hello

/msg
Type /msg nickname (message) to start a private chat.
Example: /msg Agent_Jackson Hey there, how are you?

/nick
/nick changes your nickname
Example: type /nick newnickname (limit 9 characters)

/notice
A notice is used to send a short message to another person without opening up a private window.
Type /notice nickname (message)
Example: /notice Agent_Jones Please change your nickname for this family channel.

/part
Type /part -- to leave one channel
Type /partall -- to leave all the channels you are in

/ping
Type /ping nickname. What this command does is give you the ping time, or lag time, between you and the person you pinged. Lag can be explained as the amount of time it takes for you to type your message and for others to read your messages. Unfortunately, lag is always a part of IRC, although most times it's not a problem, just a nuisance.
Example: /ping Agent_Jones

/query
Similar to the /msg, except it forces a window to pop open.
Type /query nickname (message)
Example: /query Agent_Smith Sooo....what's new?

/quit
Type /quit to leave IRC altogether. This disconnects mirc from the server.
Example: /quit Going out for dinner...nite all

/ignore
Unfortunately, there will be times when you don't want to talk to someone, or else someone may be harassing you.
Typing /ignore nickname 3, you will not receive anymore messages from that person.
Example: /ignore Benjamin 3

/whois
Type /whois nickname to see a bit more information about another user. You'll see what server another person is using, or what their ISP is. Pretty helpful when you don't recognize a nickname that wants to chat. You may recognize the IP, (Internet Protocol) and then feel more comfortable carrying on a conversation. You'll also be able to see what other channels a person is in, which might be a good indicator if you really want to talk with them or not.
Example: /whois Agent_Jackson

/chat
This opens up a DCC/CHAT window to another user. What's nice about these is that you can continue to chat even if you get disconnected from your server.
Word of Caution: Do NOT accept dcc/chats nor dcc/gets from anyone that you don't know.
Type /chat nickname.
Example: /chat Agent_Jones