Is it the current which create magnetic field, or vice versa, or both? Talking about stationary magnetic field, it is said that if a conductor rotates inside the field, a current is induced. Also, I read that current (moving charges) generate magnetic field, too. How are these connected, and what's the best approach to undertand both phenomenons?
 A: Very briefly, here is how to get started:
You are right- if a conductor experiences a changing magnetic field in its vicinity (as, for example, when it is moved past a magnet in such a way that it cuts across the magnet's "lines of force") then a current will be induced to flow in that conductor. This is called FARADAY'S LAW. 
You are also right that anytime a current flows through a wire, it will set up a magnetic field surrounding the wire. This is called OERSTED'S LAW. 
These laws are tied together in their most general form by MAXWELL'S LAWS, which show how these phenomena are mathematically related to one another on a deep level.  
You will find ample material explaining Faraday's, Oersted's, and Maxwell's laws on-line, or in an introductory book on electromagnetism.
A: 
Is it the current which create magnetic field, or vice versa, or both?

There are involved always three components.


*

*The most known case and the easiest imaginable is the Lorentz force in its primordial meaning $ \vec F = q \vec v \times \vec B $. A charge, moving nonparallel to an external magnetic field undergoes a deflection perpendicular to the plane of these two components. In the image below you read it like this: Electrons, moving into the image (electric current I], under the influence of a magnetic field B left to right, experience a force F upwards. This is how an electric device (motor) works.





*But you can reread the image as follows: A current carrying wire is accelerated and a magnetic field is induced.

*The last case: Moving a wire inside a magnetic field a current is induced. This is how an electric generator works.

what's the best approach to undertand both phenomenons?

Always think abou the three involved components I (qv), B and F.
