How does an antenna tune in a particular frequency on the receiver side?
This is a good question. 

Yes, every changing magnetic field induces a current in a conductor going through that field. That's induction for you.

Think about the most elemental antenna you can think of: the dipole. Just two sticks of metal, end to end.

When these two metal sticks sum up to be half a wavelength, all the currents align in the antenna, sum up and reach a high amplitude at the middle point. That's good, because that's where your receiver is attached, so the receiver sees a high current at that frequency.

However, for wavelengths (which is just c/f, so different frequency -> different wavelength) that don't match the antenna size, you don't get this constructive overlay: for example, for a wave with a wavelength much smaller than the antenna, the induced current mostly flows within these metal rods, and not between. 

So, antennas are naturally selective for frequencies, simply because of their geometry.

However, slight errors don't "break" reception alltogether. It just makes the antenna work slightly less well.


  And if we want particular frequency of current, we just use resonance circuit and take our signal?


Most antennas and receivers these days aren't really resonant circuits, but yeah, that's basically how it works:

The receiver filters out the frequencies that it cares about. Just like the EM waves in the air superimpose and are still dividable to their individual frequencies, this is still the case for electric signals in a wire or in a chip.