IRC stands for Internet Relay Chat, and it is a form of real-time Internet chat or synchronous conferencing. It is mainly designed for group (many-to-many) communication in discussion forums called channels. You can find out more about its history from Wikipedia
AppliedIRC has fairly strict rules on using IRC, and it is recommended that you read these before connecting to the server. You can find the rules here, or you can do the /rules command on irc to read them at any time.
AppliedIRC has their own WebChat client available for people to use to connect to the AppliedIRC server. You can access this from here. To connect to IRC, click the WebChat link and then enter your username and the channel you wish to join. The main AppliedIRC channel is #lobby. You do not need the hash (#) when typing in the name of the channel.
When you have entered your details, press connect. Another page will load (this may take some time), in which it will ask you for your username again. Just click connect. It will now connect to the server. It may be slow, be patient whilst it logs you into the server and joins you to the channel.
You may want to join another channel once you have connected to IRC. You can do so by simply typing /join #channelname (for example: /join #lobby), and then pressing enter. It'll join you to the channel as long as you have the permission to.
It is recommended that you recommend any usernames that you use on IRC. You can do this by typing: /nickserv register {password} {email} and then pressing enter. Ensure you have no curly brackets and that your password and email address are typed correctly as you will need them in the future.
You will then need to check your email to see if you have received an email from AppliedIRC, where you can take the necessary steps outlined in the email to verify your email address used. Very rarely the email will not be sent to the email address, in which case you will need to join the channel #help and speak to an oper, who will either re-send the email to you or verify your username.
If you mistype your email address whilst registering, it will be unable to be verified, and the nickname will be automatically dropped after 24 hours. You can then re-register it using the correct email.
If you would rather not wait the 24 hours, there is the ability to drop your username as long as you have the correct password. The command you need to use is /nickserv drop username password (for example /nickserv drop foo bar). You can then re-register the username with the correct email address.
Once you have registered your username, you will need to identify every time you connect to AppliedIRC. This means that you need to log in. There is a very simple command: /nickserv username password (for example /nickserve foo bar). It should tell you that you have logged in successfully once you have pressed enter.
If you are using the AppliedIRC WebChat you can simply close the window to quit IRC, or you can use the /quit command, which can have a custom message, for example: /quit I am going now, bye.