How can I build a charger for this RC helicopter?
You need a charger which is matched to the battery in your helicopter. Typically these use a single Lithium Polymer cell with a capacity of ~100mAh. To charge this properly the charger must limit current to 0.1A and voltage to 4.2V maximum. 

If a Lipo battery is charged incorrectly it may explode and burn up anything around it. This is not just theoretical. I have personally seen the results of some Lipo fires, and they were not pretty. 

An iPhone 'charger' is just a 5V power supply that simulates a USB port - the actual charger circuit is built into the phone. Some devices use an external charger, but this will be matched to the battery in the device. Unless you know exactly what you are doing, you should only use a charger with the device it was designed for (and similarly, never use a charger that was not designed for that device!).  

You could use an iPhone 'charger' or other USB power supply to run your own charger, eg. this one from Adafruit. Then you just need to attach the correct plug to suit your heli (perhaps removed from the transmitter).