이야기하다 actually a compound verb that doesn't need object. 이야기story+하다do
It simply means 'talk to' doesn't need 을/를. But if you want to, you have to add ~에 대해(about ~).
e.g., 지금, 저는 선생님과(선생님하고 같이) 한국어에 대해 이야기해요.
Right now, I am talking together with my teacher about Korean.