A friend sent me a letter asking how I was doing.

Literal

Friend [subject-が], I [topic-は] well [question-か] [quotative-と] asking letter [object-を] gave [to me-くれた].

A layered sentence: 私は元気か ('am I well?') is an embedded indirect question, wrapped by とたずねる ('asking whether') into a relative clause modifying 手紙 ('letter'). くれた marks the letter as a kindness directed toward the speaker.