And one more trick: the verb "смотреть".

When looking at a physical object, we use it with the preposition "на": смотреть на луну, смотреть на небо, смотреть на человека etc.

But when being used with some kind of art performance, this verb becomes transitives and takes accusative with no preposition:
смотреть кино (фильм) - to see a movie;
смотреть спектакль - to see a play;
смотреть представление - to see a theater performance;
смотреть балет, смотреть шоу etc.

Also: смотреть телевизор - to watch TV.

Moreover, "смотреть" is used without preposition when it means "to look thoroughly": смотреть документы, смотреть записи, смотреть журнал.
If we say: "Он посмотрел мои документы" and "Он посмотрел на мои документы", the two sentences will be understood differently:
the former means "He looked through my documents, he checked their content";
the latter means just "He looked at my documents, maybe without even opening them and without reading what is inside".

Also, we say:
Врач смотрит больного - The doctor is testing a patient (in order to diagnose).
And it is not the same as
Врач смотрит на больного - The doctor is looking (or even staring) at a patient.