Welcome to SMF! A fatty is breakfast sausage that is often packaged as "chubs". One of the brands that you hear mentioned a lot on the forum is Jimmy Dean.
Smoking a fatty can be as simple as skinning the plastic wrapper off and putting the sausage in the smoker, or you can use the sausage as sort of a blank canvas. Lots of folks put on their favorite rub before tossing it in the smoker. Most of the really creative stuff you will read about fattys is how folks stuff them.
To stuff a fatty you mash it out flat, spread on whatever you want, then roll it up like a jelly roll and seal the ends. If you do a search, you will find all sorts of Q-view (pictures) of fattys with all kinds of stuffing.
Hope this helps.
Take a little time to introduce yourself to the folks here when you get a chance.