If you have a look at the PircBot documentation, you can see the bits you might need are:
to make the connection: http://www.jibble.org/javadocs/pircbot/org/jibble/pircbot/PircBot.html#connect(java.lang.String, int)
to send the password: http://www.jibble.org/javadocs/pircbot/org/jibble/pircbot/PircBot.html#sendRawLine(java.lang.String)
I'm going to hazard a guess as I've never connected to twitch, but I'd imagine your connection lines would look like:
bot.connect("irc.twitch.tv",6667);
bot.sendRawLine("PASS oauth:twitch_oauth_token");
bot.sendRawLine("NICK yournickname");
edit:
and to answer the question in the title:
Once connected to the server, PircBot has a sendMessage(String channel,String message)
method, which will, as you would expect, send a message to the channel.