Please tell me which criteria should we use in order to find out if a reference frame is inertial or not.

In special relativity all we need to do is find out if there are any "unexpected" forces in the mix. For example, if there is some kind of Coriolis type force (just as an example) on an object then the frame is not inertial. A good fast way to determine if the system is inertial we can simply see if there are any gravitational forces acting on the system. No system with gravity acting on it is inertial. (However if the gravitational field is very weak we can still use it as inertial to a good approximation.)

The problem is, in a way, simpler in general relativity. There is always some coordinate frame such that the system is inertial, at least for any given instant. Of course, this situation is not really helpful unless you have a background in tensor analysis.

-Dan

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"I must not fear. Fear is the mind killer. Fear is the little death that brings total obliteration. I will face my fear. I will permit it to pass over me and through me. And when it has gone I will turn the inner eye to see its path. Where the fear has gone there will be nothing. Only I will remain." - The Litany Against Fear, "Dune" by Frank Herbert