How can electromagnetic waves reach a cell phone in Faraday cage?

Actually, cell phones do work in Faraday cages these days. What happens is that the conductor in the cage is not ideal, and there is some amount of leakage of electromagnetic radiation to and from the inside of the cage, specially at high frequencies. In order for the cage to be perfectly blocking it would need to have no holes at all (hence it is no longer a cage, but a box) and made of a perfectly conducting material, such as a superconductor, with a thickness larger than about 3 times the penetration depth of the radiation for that material.

The sizes of the holes need to be smaller than the wavelength of the EM radiation, so that you can neglect the holes. The wavelength is inversely proportional to the frequency of the radiation, thus, Faraday cages are more efficient for low frequencies, such as a DC field or lightning. This is why light, which is also a form of electromagnetic radiation, can pass through the centimeters-sized holes of an ordinary cage.