How can I build my own wireless charger for my cellphone?
The key for making this work is resonance. You need to make a primary resonant circuit (i.e. pure LC). Then you need to feed it AC at teh resonant frequency, not just any frequency. Third is you need a secondary resonant circuit that is tuned to the primary. Then it will work.

But beware, currents in both primary and secondary will be large. That's the whole point of making it resonant. You'll need to tune the frequency of the feeding power to be just off resonance (but close). Experiment and you'll lean a lot. These are only the basics.