You need a registered nick first. If you don't have one, see NickServ.

Why bother

Without SASL, your client joins channels first and identifies a moment later. So ChanServ doesn't give you auto-op, and channels that only allow registered users turn you away. With SASL you're identified before any of that happens. You also never have to type /msg NickServ IDENTIFY again.

Your username is your account name. That's the nick you registered, even if you're using a grouped nick right now. Your password is your NickServ password.

HexChat

Open the Network List (Ctrl+S), select IRCWorld and click Edit. Set:

User name:     yournick
Login method:  SASL PLAIN (username + password)
Password:      yourpassword

If User name is greyed out, uncheck Use global user information in the same window.

irssi

This adds SASL to the IRCWorld network from the connect page.

/network add -sasl_username yournick -sasl_password yourpassword -sasl_mechanism PLAIN IRCWorld
/save
/reconnect

Use irssi 1.2.1 or newer. Older versions have a SASL bug. Run /network to check that the mechanism, username and password are all set.

WeeChat

Assuming you added the server as ircworld:

/set irc.server.ircworld.sasl_mechanism plain
/set irc.server.ircworld.sasl_username yournick
/set irc.server.ircworld.sasl_password yourpassword
/save
/reconnect ircworld

To keep the password out of your config file, store it with /secure instead:

/secure passphrase some-long-passphrase
/secure set ircworld_pass yourpassword
/set irc.server.ircworld.sasl_password "${sec.data.ircworld_pass}"
/save

mIRC

Go to Tools → Options → Connect → Servers, select IRCWorld and click Edit. Set:

Login method:  SASL (/CAP)
Password:      yournick:yourpassword

That's the second Password box, at the bottom of the window. The account name and password go in together, separated by a colon. Needs mIRC 7.48 or newer.

Other clients

Most clients have SASL somewhere in the server or network settings. Pick PLAIN, put your account name in the username field and your NickServ password in the password field.

Did it work?

Reconnect and look at the server messages. You should see You are now logged in as yournick and SASL authentication successful before the welcome message. If you get SASL authentication failed, double-check the account name and password.