把 — what you did to the thing

把 takes the object out of its usual place after the verb and puts it in front, so the rest of the sentence can say what became of it. Textbooks call this the disposal construction, which explains nothing to anyone who has not already met it. What it does is simpler: it lets a sentence be about what happened to a known thing.

Try the first one without 把 and the problem appears: 我放书在桌子上 does not work, because the verb already has the object behind it and there is no room left for where it ended up. 把 clears that space.

The verb cannot be bare

This is the hard rule, and it follows from what 把 is for. If you have promised to say what became of the object, you have to actually say it — so the verb needs something after it: a result, a direction, a place, 了, or a doubling.

That is why 把 sentences and result complements turn up together so often. The two were made for each other.

The object has to be a known one

把 is about a specific thing — one the listener can already identify. 我把书看完了 is the book, the one we both know about. An indefinite object is odd here; if you have not mentioned it yet, use an ordinary sentence and introduce it first.

Negatives and auxiliaries go before 把

Not before the verb, which is where they would normally sit. This trips people constantly.

Verbs that refuse it

Some verbs cannot take 把 at all, and the reason is the same rule from the other side: nothing is being done to the object.

是, 有, 知道, 喜欢, 觉得, 看见, 认识 — none of them work. 我把他喜欢 is not a sentence. You cannot dispose of something by liking it.

When you would reach for it

Once you notice the pattern, it is everywhere in speech: giving instructions (把手机给我), reporting what happened to something (他把我的手机拿走了), and anywhere the interesting part of the sentence is the outcome rather than the action.