There are two kinds of commands in IRC, namely client commands and server commands. For using irchat.el it is useful to understand the difference. For example, the client command /CLEAR for clearing the screen is used in the traditional clients. This command has no effect outside your screen, and the other IRC-users need not be notified. On the other hand, the server command /NICK changes your nickname. This command affects everyone and is sent to everyone on the same channel with you (and to all servers in the network, so don't change nick without need).
In irchat.el, all the server commands are directly available. If you have set irchat-want-traditional simply by typing a slash (/) at the beginning of a line and then typing the server command with the parameters or by typing the server command in *IRC Commands* buffer and then typing C-c c. This line will be sent directly to the server (no /QUOTE needed or allowed). Notice, however, that you need to type the commands in full. So you cannot use abbreviations like /N for /NAMES. Also notice that the /M (message to user) command is really called /PRIVMSG.
For most commands, however, there is a better way. We have written emacs commands for sending the line and bound them to keys. For example, for /LIST you just say C-c l, C-c n for /NICK, C-c C-n for /NAMES and so on.
Some of there commands require parameters and they'll prompt you for them. For example, the C-c n command will ask you for the new nickname you with to use. If you at this point decide that you didn't really want to change your nickname, press C-g (control-g) to cancel.
For some commands you may give an argument but you don't have to. For
example, to see the users on channel 42, you type C-u 42 C-c w when just
C-c w would show you all users. You may omit the channel number if you
mean the current channel, that is C-u C-c w for users on the same channel
with you. To ask users on named channels like +glbf or #war
you can use C-u - C-c w, which asks the channel name in minibuffer.
C-c n works in a similar fashion.
There exists a special /QUERY-like mode, in which every line you type will be sent to one person via a private message. You begin it with C-c 2 and specifying the person to chat with, and end with another C-c 2 with blank spaces as the name of the person.
There are two other ways for sending private messages, C-c p and C-c m. With C-c m you'll be asked for the name of the person and then for the text. You'll be typing the text in the minibuffer. The other way is to type the text in the command buffer, and to press C-c p to send it. irchat.el prompts you for the name of the person to send it to, the default being the name of the person you sent your last private message to. You can easily chat privately with two persons at a time by being in a C-c 2 with one and C-c p:ing with the other.
When you join a channel, completion is also available. C-c j +mTAB takes you to the channel +My_very_long_channel_name, if there happens to be such a channel. You can also join a channel where some person you know is, just use C-c j mta and you would be on channel where user mta is.
Notice that for C-c m, C-c p, C-c 2, C-c f (/WHOIS), and C-c k (/IGNORE) nickname completion is available. What this means is that you only need to type a few first letters of the nick, and you can use TAB or SPC to fill in the rest. This feature is also available in the command buffer, bound to C-i (TAB), where it completes the word you typed last assuming it is a nickname. This is handy for typing long nicks so that you get the CaSe correctly. For example, to say "BigCheese: ..." you just need to say "biTAB:", assuming nobody else (on IRC at the time) has nick that starts with bi.