How can you get a Logitech Harmony 880 remote to control a Harbor Breeze Triton ceiling fan?

If the harmony website doesn't have a device listing for your fan, then you need to learn it. With the remote plugged in, and the harmony software running, you can select 'learn new command' somewhere in the menus. When it asks you to, point the original ceiling fan remote towards the back of the harmony, and teach it the buttons you wish to use. If you don't have the original fan remote, you may not be able to control it.

Actually the main problem here is the 880 is not an RF remote and the Triton is an RF Fan.

I use URC products so I am not sure what Harmony offers other than upgrading to the 890 remote.

All you need to do is get something to translate your IR remote signals to RF for the fan.