I have had some trouble sorting this out myself. My understanding is that the subjects yo, tú, nosotros, are not necessary because the verb conjugation makes clear who or what the subject is. Sometimes a subject is used to add emphasis, such as "Yo hablo," to stress the fact that the subject, and not someone else, is expressing themselves at the moment.
I have noticed that sometimes the Rocket Spanish conversations use a subject, while other times, for no apparent reason, they do not. An example can be found in lesson 6.5. One sentence says "Nosotros estamos corriendo," while another says "Estamos bebiendo la cerveza." My tutor, a native Spanish speaker, tells me that even though the subject is not needed, it is not wrong nor does it make the speaker sound inarticulate, to include the subject. I take this as evidence that language is an art rather than a science, and so does not operate by strict rules, but more with guidelines.
If the subject of the sentence is not clear from the context, the subject should be used to prevent ambiguity.
This is what I think I know. Hopefully some of the more advanced students here will clarify or correct me.