Giver は/が + Receiver に + Object を + あげる
あげる means "to give" and is used when the speaker (or someone in the speaker's in-group) gives something to another person. It can also describe one third party giving to another third party.
The basic pattern is:
Giver は/が + Receiver に + Object を + あげる
A key distinction in Japanese is who is giving to whom:
Compare: 田中さんは私に本をくれた。 (Tanaka-san gave me a book.)
Because of this directionality, あげる should not be used when someone gives something to the speaker. Using あげる in that situation is a common mistake for learners.
When giving to a social superior (a teacher, boss, etc.), the more respectful form さしあげる差し上げる (さしあげる) is often preferred over あげる in formal speech.
あげる is also common when giving food or water to animals or plants.