The grammar pattern Verb + てあげる presents an action as something done for someone else’s benefit. The giver is usually the speaker or someone on the speaker’s side, and the receiver is another person.
Formation
Verb て-form + あげる
教えてあげる
"teach someone"
Person + に + Verb て-form + あげる
友達(に説明(してあげる
"explain it for a friend"
Note: に marks the person who receives the benefit.
Verb て-form + あげて
仲良(くしてあげて
"be nice to them"
Note: The て-form can be used when asking or telling someone to do the beneficial action.
Perspective
With 〜てあげる, the action moves away from the speaker’s side toward someone else.
シャロがチノに教(えてあげる。
Sharo teaches Chino.
あげる adds that Sharo is doing it as a favor or helpful act for Chino.
Giver and Receiver
The giver is often omitted when it is the speaker. The receiver can be marked with に.
妹(にお弁当(を作(ってあげた。
I made a lunch for my little sister.
The plain action is making a lunch. 〜てあげる adds the direction of benefit toward the little sister.