[subject] + 给 + [person] + [thing] [subject] + 给 + [person] + [verb] + [object]
给 as a verb means "give", and it takes two objects in a row: the person, then the thing.
The order is fixed. English allows "give a book to you"; Chinese puts the recipient first with nothing in between.
In front of a verb, 给 marks who the action is done for or to. It goes before the verb, not after.
不给 for a refusal, 没给 for something that did not happen.
Some verbs take 给 on the other side: 送给, 卖给, 还给, 借给. The recipient follows.
给我 on its own is an instruction to hand it over, and sounds abrupt without 请 or 吧.