Something I have observed during my lessons is that some students try to bring Russian structures into English, and I recognize it is part of the learning process. However, we need some language awareness, so today I'll take into account only one of those mistakes, which is confusing or omitting prepositions. This is often difficult because English and Russian expressions often have prepositional phrases that seem to be the same but are in fact different. Here are two of commonly confused prepositions:
Depend on — зависеть от — 
not depend of Divide into — разделить на — not divide on
In addition to using the wrong preposition, some English expressions may not require a preposition when one is necessary in Russian and vice versa:
To wait for someone (ждать кого-то)
To graduate from school (законтчить школу)
To listen to someone/music (слушать кого-то/музыку)
To be afraid of someone/something (бояться кого-то/что-то)
To explain to someone (объяснить кому-то)
To answer a question (ответить на вопрос)
Finally, there are some common categories of prepositions that can be helpful to understand.
Surface: ON (table, wall, floor, plate, roof, face, shelf, etc.)
Technology: ON (computer, TV, radio, screen, DVD, hard drive, CD etc.)
Large transport: ON (train, bus, tram, plane, ship, ferry, etc.)
Inside a physical object/structure: IN (book, newspaper, hat, drawer, pocket, box, room, etc.)
Places: AT / IN (office, stadium, shop, supermarket, station, theater, park, etc.)
Well, I hope those hints can help you somehow! See you around.
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