In addition, "speak" can be more physical/mechanical.
Please speak louder. The students in the back can īt hear you. As Alicia said, talk is more like conversar. It tends to deal with the human interaction involved, while speak leans more to the fact that words are coming out of your mouth.
We teach a dog to "speak."
We teach a parrot to "talk."
There are, of course, only generalizations.
"Don īt interrupt when I īm speaking" deals with the action taking place.
"Don īt interrupt when I īm talking" deals with the conversation (interaction) taking place.
"A policeman is coming to speak to the class" brings a picture of a formal lecture.
"A policeman is coming to talk to the class" sounds more interactive and conversational.
(This is similar to what hongduyen said)
I hope this helps.
Bruce