Do you want to come up with your own circuit, or do you need to make a metal detector circuit somehow? If the case is the later, read about BFO (Beat frequency oscillation). It is the easiest method to build a metal detector. You will be feeding two frequencies(from oscillator circuits) into a frequency mixer chip. You can set the mixer to give you the difference in frequency as an output. This difference will then be amplified and fed into a speaker. You will have two coils of course, one in each of the two oscillators. One coil will be your detector coil, when it comes in proximity with metals, its inductance will change causing the the frequency to change in one of the oscillators, which is turn, will generate a difference frequency you can amplify and hear. Of course you will have to design your two oscillators to have the exact same frequency at the initial condition.
Hope this helps.