[noun (person)] + に + [verb て-form] + もらう
てもらう says someone does something for you, told from your side: "I had ~ do it", "I got ~ to do it". It follows the て-form. You, the receiver, are the subject and usually go unsaid, and the person who does the favour takes に.
The doer takes に, never が. With が they would be the one receiving the favour.
Both describe the same favour. てくれる makes the doer the subject with が; てもらう makes you the subject and puts the doer on に. てもらう often, though not always, suggests you asked for it.
The potential てもらえる turns it into a request: "could I have you ~?". The negative question てもらえませんか is softer still.
With someone above you, use the humble ていただく in place of てもらう, and ていただけますか to ask.
These go beyond a favour received.
てもらいたい says you want someone to do something for you.
When what you get is passed on to you – something taught, something sent – the doer can take から as well as に.