Please give me that one.
Please give me two apples.
Please give me a million yen.
You know that the kanji 下 means down and that さい sounds like the word "sigh." You need to ask someone for something, so you look down, sigh, and say please give me that thing. You're ashamed that you have to ask. But you still need it. Please, please give it to me!
We only use this kanji version of ください when we're asking for something, that's why it's "please give me." If you're just saying "please" you don't need the kanji at all!
The reading for this word is an exceptional reading. You just have to be able to recall the くだ part, though (since さい is already there in the form of the hiragana). So, think about why you have to be polite to this misbehaving kid. Turns out, if you don't, he has the power to initiate a Coup d'état against you and your family, who runs the government. Just imagine yourself thinking over and over "Okay... I have to be nice to this kid. If I don't... he'll initiate a Coup d'état... and that would ruin my family..." You're walking on thin ice, here.