Learn Hardcore Japanese: kami wo tukue no ue ni oite kudasai.

In Japanese, を marks the direct object of a verb—in this case, 紙 (the thing you’re placing). に marks the destination or location where something is placed—here, 机の上 (on top of the desk). Together they tell you “put the paper (を) on the desk (に).”

Can I change the word order to say 机の上に紙を置いてください?

Yes. Japanese has flexible word order, so 机の上に紙を置いてください is actually more common and sounds perfectly natural. You could even emphasize the paper by saying 紙を机の上に置いてください or the location by saying 机の上に置いてください紙を, though the last one is unusual in polite speech.

What does the particle の do in 机の上?

の connects two nouns in a possessive or descriptive way. 机の上 literally means “the top (上) of the desk (机).” It’s like the English “of” or the ’s construction (“desk’s top”).

Why is the verb 置く in the form 置いてください instead of the plain 置く?

置いてください is the て-form of 置く plus ください, which turns it into a polite request (“please put”). The plain form 置く would be dictionary form (“to put”) and doesn’t express a request.

What’s the nuance difference between てください and the plain imperative form?

てください is polite and gentle—“please do X.” The plain imperative 置け is abrupt and can sound harsh or bossy, so you usually avoid it unless you’re very familiar with someone or in a commanding situation.

Why is there no subject in this sentence?

Japanese often omits the subject when it’s clear from context. In English you’d say “You put the paper…,” but in Japanese it’s understood you’re addressing the listener, so あなた (you) is left out.

Can I use お願いします instead of ください?

You cannot directly attach お願いします to a verb. Instead you’d say 紙を机の上に置いてお願いします, which is ungrammatical. If you want to use お願いします, you can say 紙を机の上に置いて、お願いします, but it’s more natural to stick with 置いてください for verb requests.

Could I shorten it to just 紙を置いてください if the location is obvious?

Yes—if your listener already knows where the desk or spot is, you can drop 机の上に and say 紙を置いてください (“Please put the paper”). Leaving out obvious details is common in Japanese.