How was the friend raised by his/her parents?
pre-masu form + 方【かた】 forms a noun phrase meaning "way of ～", or "how ～". For example 食べ方 is "the way of eating it" or "how to eat it". Combined with some adjectival expression, it also works as a suru-verb. For example 彼は面白い考え方をする means "His way of thinking is interesting".
- 育てる: "to raise (a child)"
- 育てられる: the passive form of 育てる, "to be raised"
- 育てられ: the pre-masu/continuative form of 育てられる
- 育てられ方: "the way of being raised"
The subject of the whole sentence is 友達, but I believe 友達 should be marked with は because it must be a definite person, i.e., 友達 must have been introduced in the universe of discourse.