HELP!

The man was killed BY or WITH a knife? Which one is correct gramatically?

killed by a person (alive)

killed with an instrument  (inanimate)

good

Although a bus is not inanimate, I think most Americans would say killed by a bus, hit by a bus. Perhaps it is the ability for a bus to move.

yeah that's true – killed by a bus, killed by a car

 run over by a bus, run over by a car 

Also, you can say "Death by poison, Death by stabbing, etc."

A good way to test phrases like this is to go to Google, change the language to English (in the Advanced Search, there is a language choice option), and enter the phrase in quotes (very important!).

"killed by a knife" – 663 hits

"killed with a knife" – 16,900 hits

Therefore, "killed with a knife" wins the Googlefight! 

I also often use Google to test English phrases or collocation samples I am not too sure about.

by for people and with for instruments….right.

About animals?

I've read in somewhere " a man was bited by a dog".

Is it right?

" a man was bitten by a dog".

yeah – "by a dog" is correct.

Well, it's valid for humans also – A part of his ear was bitten off by a boxer.

for me the biggest problem is with prepositions. I'm studying English for many years and I still have problems with deciding when to use "the", "a/an" or no preposition at all.

Is there any key to solve my problem, or I shold practice more?

An apple. A pig.

If the next word starts with a vowel, you use "an. If the next word starts with a consonant, then you use "a".