1) "mi" is a possessive, same to English my. Mi casa (my house) mi amigo (my fiend)
2) "soy" is the first person singular of the verb "ser" (to be) yo soy= I am. As you may know, in Spanish we have two different verbs to describe the two different meanings of to be: ser for the attributes of the being (soy bueno= I'm god) and "estar" for the permanence in a place or in a state of being (estoy en la oficina = I'm in the office / estoy enfermo= I'm sick). This is a problem for most students, and cause of common mistakes.
Regarding the different first person pronouns, in Spanish there are only two:" Yo" equal to English I, and "me" which is equal to English me , but the pronunciation is different: In Spanish is "me" with e like in elegant.
"He was talking to me " El me estaba hablando".
Then, we can combine "me" with other pronouns like lo and la (designing masculin and feminine entities, both persons and things) in order to create pronominal combinations : "me lo dió ayer," ( he or she gave me yesterday something of the masculine gender) "me la enseñó esta mañana" ( this morning, he or she showed me something of feminine gender)
In English we should say: He gave it to me yesterday, no matter if it is a book or a motorcicle.
I know: English is easier !