"His friend speaks about me."
Translation:El amigo de él habla acerca de mí.
This does not help - you are saying what we already know. We want to know why?
me is used with reflexive verbs, direct, and indirect objects.
"Yo me ducho." (reflexive verb) "Ella me abrazó." (direct object) "El me mandó una postal." (indirect object)
mí is used in prepositions.
"Ese regalo es para mí." (object of preposition)