"I put a table in the room."
That's true, but I think in actual use, I think people say "I am putting" unless they're describing a process they repeat a lot, like "I put dirty dishes in the dishswasher." If someone was moving a table and told me "I put a table in the room" I'd be confused because they haven't put it there yet. they're still putting it there.
に is always (hate using that word as there's sure to be an exception to pop up and prove me wrong) for location (either in time or place). It's easy to remember if you think of it as "in" because "in" and "ni" are inverse of one another. However, it doesn't always translate to the word "in"; so be careful with that. Ex: (Place/location/timeframe)に... In the room = へやに...
を is always used after that object that the action (verb) is being done to. Ex: objectをverb. I eat the apple. りんごを食べます。
I hope that helps!
"Wo" marks a word as receiving the action of the verb. In English this is often the direct object. "Ni" marks some indirect relationship with the verb which can be any of several logical associations. "Wa" marks a topical relationship to the verb which is often that of the subject but it can also be the object. "Wa" throws the emphasis toward the word it marks and "ga" throws the emphasis toward the verb.