I have made handles one way my whole life. Roll out a carrot of clay, pull a handle (like milking a cow, sort of) then let is dry a bit then attach. Someone showed me how to do the whole thing differently and more directly---place the carrot onto the pot, then pull. It looks a little different, because it grows right off the piece. I think it is useful for some pieces, and the way I have made them before is better for other pieces. Anyway, here is the happy potter and a mug handle, start to finish.
Thanks to missus Pottersblog for these pics.