How do we know prophets are prophets? Some like Elijah, and Moses, can create miracles, like Jesus. Many of the miracles are not that public though. Still, it's reasonable.

Some, like Abraham have "voices" in their head. Most of the time, we call those people shizoprenia.

What do we know about each prophets and how do people there knows that he is a prophet?

An easy way to pinpoint false prophet is to see if the prophecy is false. But how to identify true prophet.
The prophets of the Old Testament frequently brought warnings, adjuring the people (or the recipients of the message) to change...or else.


  Deuteronomy 18:22 (NASB)
  When a prophet speaks in the name of the LORD, if the thing does not come about or come true, that is the thing which the LORD has not spoken.


This is the real test of any prophet.

The prophets frequently performed miracles or knew things that they couldn't have known (Nathan, 2 Sa 12:7) to prove that they were from God. Some had already an already established reputation as a prophet (i.e. Elijah, Elisha, ...) and didn't need to prove it every time they delivered their messages. 

I suspect that in addition to these things, the people to whom the messages were sent could tell that the message was real because it rang true in their consciences. Typically, when God tells people to do something (as opposed to warning them about their sin), he adds a miracle as a "signature." (Is 38:8)