How would I go about making a trigger (E.g. !Help) and then the bot will private message them a list. Not the type of message where it will open a new window, but where it will show in the channel but only them can see it (if you know what I mean.) I don't know the terms with these, so any help would be great.
The message you're talking about is one sent by using the /msg <User> message command as opposed to one using /query. As explained here (section 2.2 Private conversations):
In mIRC, if you initiate a /MSG you don’t get a “query” window until the other person responds to you. You can set up a “query” window on your side right from the beginning by using the /QUERY command.
The thing is, as this is client specific behavior you can never be sure a client that isn't mIRC will behave one way or another.
With that out of the way, coding-wise, what you most likely will want to use is a python irc protocol client library that will save you the trouble of dealing with the IRC protocol plumbing. That particular library brings you an example irc bot, which is probably the point where you'd need to start.
Good luck.