あげる・くれる・もらう details

Examples

give — あげる sends the thing away from the speaker's side, くれる brings it in

これ、母ははがくれたお菓子かし。よかったら食たべて。

kore, haha ga kureta okashi. yokattara tabete.

These are sweets my mum gave me — help yourself. casual

誕生日たんじょうびに、妹いもうとに手袋てぶくろをあげました。

tanjoubi ni, imouto ni tebukuro o agemashita.

I gave my little sister gloves for her birthday. neutral

ご来店らいてんのお客様きゃくさまには、粗品そしなを差さし上あげております。

go raiten no okyakusama ni wa, soshina o sashiagete orimasu.

We are giving a small gift to every customer who visits the store. formal

receive — もらう makes the receiver the subject, and に or から marks who it came from

先輩せんぱいに古ふるい自転車じてんしゃをもらったんだ。

senpai ni furui jitensha o moratta n da.

I got an old bike from an upperclassman. casual

面接めんせつのあとで、会社かいしゃから詳くわしい資料しりょうをもらいました。

mensetsu no ato de, kaisha kara kuwashii shiryou o moraimashita.

After the interview I received detailed materials from the company. neutral

先生せんせいから貴重きちょうなご意見いけんをいただきました。

sensei kara kichou na go iken o itadakimashita.

I received valuable comments from my professor. formal

恐おそれ入いりますが、こちらの申込書もうしこみしょをもう一枚いちまいいただけませんか。

osoreirimasu ga, kochira no moushikomisho o mou ichimai itadakemasen ka.

I'm sorry to trouble you — might I have one more of these application forms? formal

くれる lands on your in-group — family, colleagues, your own company — and
あげる never does: ×田中たなかさんが私わたしに本ほんをあげた. Between two
outsiders it is あげる.

ていただけませんか
The bare verb asks for a THING (申込書もうしこみしょをいただけませんか), the て-form for an ACT (書かいていただけませんか) — the politeness is identical, and only what is being asked for decides which one a counter uses.
てくれる
The bare verb hands over a THING (ノートをくれた), the て-form hands over an ACT (ノートを貸かしてくれた) — and Japanese requires the second one where English drops "for me" altogether.
てもらう
もらう with an object reports a transfer and nothing more; 〜てもらう adds that the receiver invited the favour, which is why a stranger's unasked kindness goes to 〜てくれた instead.
てあげる
Only the て-form carries the patronising edge — あげる with an object is neutral (お土産みやげをあげた), while 持もってあげましょうか aimed upward advertises the favour and has to become お持もちしましょうか.

に
One に, two opposite roles — 友ともだちにあげる makes the friend the destination, 友ともだちにもらう makes them the source; から may replace the source に (先生せんせいからもらう) but never a recipient に, so 友ともだちからあげる can only mean the friend is the giver.
〜上げる・〜上がる
The same verb in two frames — 書かいてあげる puts the writing at someone else's service, 書かき上あげる finishes it; the て-form marks the favor and the ます-stem the completion, and nothing else tells them apart.