"I send a letter to my friend."
Translation:저는 친구에게 편지를 보냅니다.
I understand that you mean "to friend" not "to letter", but it is easier do on paper than on these comments. I am trying a different way but based on your following the Korean wird order.
저는 친구에게 변지를 보냅니다.
S = SUBJECT: I
Indirect object + particle: friend+to
O = direct OBJECT: letter
V = VERB: send.
Any friend that I send a letter to is by default "my" friend. Maybe that possessive word is understood in Korean and English, not needed until we want to express closeness. Or to make certain whose friend. In a mystery show's dialogue, it might be a clue. Poirot or Agatha might wonder why was the speaker so impersonal and did not use 저의.