Japanese picks the verb by which way the thing moves relative to you: あげる away, くれる toward you, もらう you receiving. The same three verbs then attach to the te-form to talk about favours.
Also known asageru kureru morauあげる くれる もらうgiving receiving japanesete ageru
に marks the receiver, を the gift: 友達に 花を あげます.
わたしは ともだちに はなを あげます。
I give flowers to a friend.
あげます = “give”. The receiver is marked with に, the thing given with を. あげます is used when the giver is the speaker or someone close to them.
In the textbooksMinna I, lesson 7
に marks the source you receive from: 友達に 本を もらいました.
ともだちに ほんを もらいました。
I received a book from a friend.
もらいます = “receive”. The person you got it from is marked with に (から is also possible). Contrast with あげます, where に is the receiver.
In the textbooksMinna I, lesson 7
て-form + あげます = do a favour for someone else.
わたしは ともだちに ほんを かして あげました。
I lent a book to my friend (as a favour).
て + あげます shows the action benefits someone else, done by the speaker or their side. Be careful: said directly to a superior it can sound condescending.
In the textbooksMinna I, lesson 24
て-form + くれます = someone does a favour for me/my side.
ともだちが てつだって くれました。
My friend helped me (for my benefit).
て + くれます is used when someone does something for the speaker (or their in-group). The doer is marked with が; the speaker as beneficiary is usually unstated.
In the textbooksMinna I, lesson 24
て-form + もらいます = receive the favour of someone doing something.
わたしは ともだちに みちを おしえて もらいました。
I had my friend tell me the way.
て + もらいます is from the receiver's viewpoint: I get someone (marked に) to do something for me. くれます marks the doer with が; もらいます marks them with に.
In the textbooksMinna I, lesson 24
The humble version of 〜てもらう: I receive the favour of someone (に) doing.
せんせいに さくぶんを なおして いただきました。
I had the teacher kindly correct my essay.
Use 〜ていただきます when the person doing you the favour is someone you should be polite to. The doer takes に (or から). It's the humble counterpart of 〜てもらいます.
In the textbooksMinna II, lesson 41
The honorific version of 〜てくれる: a respected person does something for me.
ぶちょうが てつだって くださいました。
The department manager kindly helped me.
くださいます is the honorific of くれます — used when the giver of the action is someone of higher status. The doer takes が. To give to a lower-status person/animal, use 〜てやります.
In the textbooksMinna II, lesson 41