When给 is a preposition:
给 + the object of an action
导游给我们介绍了这里的历史。(Dǎoyóu gěi wǒmen jièshàole zhèlǐ de lìshǐ.) The tour guide introduced us to the history here.
我给大家说了为什么迟到。(Wǒ gěi dàjiā shuōle wèishénme chídào.) I told everyone why I was late.
孩子给妈妈唱了一首歌。(Háizi gěi māma chàngle yī shǒu gē.) The child sang a song to the mother.
The object could be the receiver, for the benefit of; for the sake of; for.
我给弟弟买了一个足球。(Wǒ gěi dìdi mǎile yīgè zúqiú.) I bought a football for my brother.
你给女朋友买一些花吧！(Nǐ gěi nǚ péngyǒu mǎi yīxiē huā ba!) Buy some flowers for your girlfriend!
>> It indicates getting something (concrete) from someone.
老师给学生们提供了帮助。(Lǎoshī gěi xuéshēng men tígōngle bāngzhù.) The teacher provided help to the students.
我给大家介绍了一个新朋友。(Wǒ gěi dàjiā jièshàole yīgè xīn péngyǒu.) I introduced a new friend to everyone.
>> It indicates giving or getting help or benefit from someone.
The object could be someone who has lost something.
我的钱，她全给我用完了。(Wǒ de qián, tā quán gěi wǒ yòng wánle.) She ran out of my money.
这么多水果，他全给我吃光了。(Zhème duō shuǐguǒ, tā quán gěi wǒ chī guāng le.) He ate up all of these fruits of mine.
>> It indicates losing something.
下雨了，衣服都给我淋湿了。(Xià yǔle, yīfú dōu gěi wǒ lín shīle.) It’s raining and the clothes are getting wet.
对不起，自行车给你弄坏了。(Duìbùqǐ, zìxíngchē gěi nǐ nòng huàile.) Sorry, your bicycle was broken.
>> It indicates losing some benefit or advantage.
The object could be the one that somebody serves for.
服务员给我加了热水。(Fúwùyuán gěi wǒ jiāle rè shuǐ.) The waiter added hot water for me.
司机给我打开了车门。(Sījī gěi wǒ dǎkāile chēmén.) The driver opened the door for me.
Verb + 给 + Object
Verb + （给） + Object
这些东西不能借（给）你，但是可以卖（给）你。（Zhèxiē dōngxī bùnéng jiè (gěi) nǐ, dànshì kěyǐ mài (gěi) nǐ.）These things cannot be lent (to) you, but they can be sold (to) you.
我想还（给）他钱，但是他不在家。(Wǒ xiǎng huán (gěi) tā qián, dànshì tā bù zàijiā.) I want to pay him back, but he is not at home.
When the verb doesn’t imply the meaning of “giving”, 给 could not be omitted.
Verb + 给 + Object
你能唱歌给我们听吗？(Nǐ néng chànggē gěi wǒmen tīng ma?) Can you sing to us?
这是她写给我的信。(Zhè shì tā xiě gěi wǒ de xìn.) This is a letter she wrote to me.
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昨天学的”我给忘了”… This is so hard for me to grasp. I fail to conceptualize the logic behind it.