Being slightly more direct than てくれる, てもらう removes the meaning of ‘to bestow’ (to the speaker), and focuses on the meaning of ‘to receive’ (from the giver). With てもらう, に will mark the person that ‘did something’ for the subject, while が (or は) will highlight the receiver themselves.
In English, this grammar structure is regularly translated as ‘to have (someone) do (A) for you’, or ‘to get (someone) to do (A) for you’. Literally, it means ‘to receive the action of (A)’.

• 日本語（にほんご）が話（はな）せないから友達（ともだち）に行（い）き方（かた）を聞（き）いてもらう。
  Because I can't speak Japanese, I'm going to have my friend ask for directions on my behalf.
• 私（わたし）は虫（むし）が嫌（きら）いなので妻（つま）に虫（むし）を捕（と）ってもらう。
  Since I hate bugs, I get my wife to catch them.

てもらう is also regularly used when receiving a service from someone, as てくれる would imply that the action was a favor.

• 昨日（きのう）は朝（あさ）から頭（あたま）が痛（いた）かったから医者（いしゃ）に見（み）てもらった。
  Because my head hurt since the morning yesterday, I had a doctor look at it.
• 朝（あさ）から頭（あたま）が痛（いた）かったから病院（びょういん）に行（い）って、医者（いしゃ）に見（み）てくれた。
  Because I had a headache since this morning, I went to the doctor and he checked it out for me.