Used to indicate a device or machine, such as a phone or computer:
He is on the phone right now.
She has been on the computer since this morning.
My favorite movie will be on TV tonight.
Used to indicate a part of the body:
The stick hit me on my shoulder.
He kissed me on my cheek.
I wear a ring on my finger.
Used to indicate the state of something:
Everything in this store is on sale.
The building is on fire.
We use this preposition when we talk about the completion of some activity, e.g.: По завершении эксперимента мы написали монографию. - On the completion of the experiment we wrote the monograph.
We use this preposition in the meaning of about in the titles, e.g.: О разложении металлов. - On the decomposition of metals.