What determines the direction and cause of electric field exerted on test charges?
However, I can't understand why and how we know the main electric field is + or - charged?


One way is to place free test charge in the field and see which way it moves.

One instrument that essentially does this is the electrometer.


  What causes it?


In physics textbooks, we an study a case where a single charge sits in an infinite universe with no other charge, producing an electric field that radiates away from it in all directions with perfect symmetry.

In the real world, we almost always deal with situations where charge is balanced. There is a negative charge somewhere to terminate whatever field emanates from a positive charge and vice versa.

So if we see an electric field pointing from A to B, there is almost always a positive charge somewhere in the neighborhood of A, and a negative charge near B.


  For instance, what causes and determines the direction of electric field in a DC power line?


Whoever designed the power system designed the system to produce either a positive or negative voltage on the line (relative to earth). 

If they produced the DC voltage by rectifying an AC source (like a generator), then they can choose the polarity of the DC voltage by how they connect the rectifier to ground.

If they produced the DC voltage from a battery, then the chemical reactions going on in the battery determine which terminal is positive and which is negative. We can connect our power line to either of these and connect the other to earth (and possibly also to a return conductor) to get whatever polarity we want on the DC power line.