Now I see.
The process is fairly simple with Chatzilla. It's the 'help' that you get that is incredibly archaic and convoluted.
The first thing I learned that had to be done when downloading Chatzilla, is to go to the menu chatzilla>preferences... and there you will find that chatzilla has used your computer name as your nickname and user name. Since I am going to go on the ubuntu-us-nm chat, what it needs to display is my ubuntu user name (the site uses a form of identification and if you are not an Ubuntu user, it seems to reject you.) Now back to the main chatzilla window. You will see a lot of stuff, but the main thing is the llist of servers supported by chatzilla. click on 'freenode'. There will be a quick load of a lot of stuff,which, unless you are a history buff,probably isn't going to be of importance to you. Down below the main window is a smaller window where you can type stuff. On the right side of the page is an arrow with a ninety degree bend pointed toward the typing area. After you type stuff that you want to enter, you click on that arrow and it will send it (hitting enter just sends you to the next line to be typed)
Once you are in 'freenode' type in the following---
/join #ubuntu-us-nm
Then you click the bent arrow and the main page will display the ubuntu nm chat.
I can't say how it works in other irc chat clients because, as newbie, sorting this thing out without any input from others, I am just trying to follow the normal Linux path to gaining knowledge,ie; try everything until you find something that almost works and figure that is 'goodenough'.
If anyone knows of a better way I hope that they will post it here and share the knowledge.