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I have yet to find a good source that covers this in full. But I've seen them
being used in places where no giving or receiving is taking place. For
example,

> "写真をとってもらえませんか？"

and another one I saw just now on this stack exchange:

> "私が子供の時、母がこの本を読んでくれました。"

From what I can see, nothing physical is given or received, and in the case of
the second book, what was given/received?
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question
words subsidiary-verbs giving-and-receiving
How to use あげます、もらいます、and くれます
あげます is to give, もらいます is to receive and くれます is also to give.

[![Here is the sentence formula for あげます and
もらいます](https://i.stack.imgur.com/A8Q8i.png)](https://i.stack.imgur.com/A8Q8i.png)

For example

> **あげる**
>
> 先生はエリコに本をあげました。  
>  The teacher (giver) gave a book to Eriko (recipient)
>
> * * *
>
> **もらう**
>
> エリコは先生に/から本をもらいました。  
>  Eriko (recipient) received a book from the teacher (giver).

For くれる, it's the same sentence formula as あげる, but used like this:

[![enter image description
here](https://i.stack.imgur.com/kcHRa.png)](https://i.stack.imgur.com/kcHRa.png)

Here are some examples:

>   1. あかつねはエリコに花を **あげました。**  
>  Akatsune gave Eriko a flower.
>
>   2. あかつねは弟に花を **くれました。**  
>  Akatsune gave a flower to my younger brother.
>
>   3. 母はエリコにお茶を **あげました。**  
>  My mother gave Eriko green tea.
>
>   4. お兄さんはわたしにプレゼントを **くれました。**  
>  My older brother gave a present to me.
>
>   5. わたしは父にコーヒーを **あげました。**  
>  I gave my father coffee.
>
>
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I think he might have asked whether the person was asking for permission or
whether it was about making a request.

> 写真をとってもらえませんか

Is that asking for permission to take a photo, or asking someone to take a
photo for them?!?

I think when morau comes after a -te verb, then it becomes a request. So
basically, "Can you take a photo for me?"

  * `totteageru` -- Can you let me take a photo for you/someone else 
  * `tottekureru` -- Can you take a photo for me? And then give to me 
  * `tottemoraemasenka` -- Could you let me take a photo? Simply giving the person permission to take a photo. Who will get the photo afterwards is irrelevant.

_ADDED LATER_

not entirely true. <http://jisho.org/search/moraeru>. If this is to be
believed, it could also mean something like. 俺に写真を取ってもらえませんか. if the おれに is
specified, then it could mean "Could you take a photo ( and give it to me)
please? However, morau for example doesn't necessarily explain whether you are
letting someone do something or forcing someone to do something. It simply
says that you (by whatever mean) HAVE someone do something. So then it would
be like "Could I have you take a photo? The person with the camera who asks
the permission wants the photograph, but is not asking for permission, simply
the favor of taking the photo, and if oreni is declare, then it means to ask
the favor of taking the photo, then giving it to me. So morau has more to do
with favors, not permission. Give me a biscuit, a favor, not a question of
permission. You are already seated so you are entitled to the cookies.

So morau is more the favor of giving to me. Ageru is permission to do
something for someone, and kureru is permission to do something.

> 君が俺に写真を取ってもらえませんか Could you take a photo (for me)  
>  俺が写真を取ってあげますか Am I allowed to take a photo (for you)  
>  君が俺に写真を取らせてくれませんか Would you allow me to take a photo (for me/or someone
> else)

There you got it.
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When あげる, もらう and くれる are used with the ～て form, they basically keep the same
meaning as they ever do, as explained in @Silfrost_Wolf20's answer.

The only change is that there is no "object" given or received but a favour
described as an action.

For instance,

> 写真をとってあげましょうか？
>
> ~~写真をとってもらえませんか？~~ (as per @chocolate comment)

asks someone if they would like to receive (from yourself) the favour of
taking a photo for them, translated as

> Would you want me to take a photo of you?

On the other hand,

> 写真をとってくれませんか？

asks someone if they would not mind giving you the favour of taking a photo,
translated

> Could you take a photo of me/us please?
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If you ask what is given/received, _favor_ is a likely answer, as we say "do
somebody a favor" in English. Actually, when they're used as subsidiary verbs
(補助動詞), they never literally mean "give" or "receive".

Basically, **any** action A does to B that satisfies B's desire/intention is
qualified to take one of ～てあげる／もらう／くれる according to the relation between the
giver and the given in the sentence.

  * あげる: _give_ (the subject is A), _outbound_ ( **I/WE** → **YOU** → **OTHERS** (→ **OTHERS** ))
  * くれる: _give_ , _inbound_ ( **I/WE** ← **YOU** ← **OTHERS** )
  * もらう: _receive_ (the subject is B), no directional difference

But in actual world, be careful using ～てあげる for your own deed. It assumes your
action has benefited the receiver, so you could be felt patronizing unless
it's clearly profitable.
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answer
写真をとる: To take a picture.

もらう:To receive.

写真をとってもらう: Literally: to receive the action of taking a picture.

写真をとってもらえますか？ Could you take a picture for me?

The verbs もらう and all its variants (あげる, くれる, etc) can be used not only for
objects but for actions.
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