A 9v battery is not good for anything that needs so much current like you old cell phone. You can certainly learn how to build a DC/DC converter but even with that the current needed from a 9V battery will exceed 100 mA while 20 mA is a heavy load for such battery.
All that is why cell phones use special Li-ion rechargeable batteries no other battery type can compete. For 3.7 V you can use an emergency (short-life) power supply of three AA alkaline cells but a regulator to 3.7 V is needed. Find some suitable 1A voltage regulator at Mouser or Digi-Key.