The circuit uses the IC1 which is the CD4011 and the IC2, the CD4023, both of these are logic ICs. The reference generator is implemented in two logic elements of the integrated circuit IC2. Its frequency is stabilized and is determined by the quartz crystal X which is 1MHz. The generator with a variable frequency is made on the first two elements of the IC1. The oscillating circuit here is formed by the search coil L, the capacitors and the varicap. The potentiometer 10K is for tuning to a frequency of 100kHz, this actually sets the required voltage to the varicap VD1.
The circuit use the signal logic elements IC1-3 and IC2-3 as buffer amplifiers and the signal mixer is the IC1-4.
The speaker should be a high resistance phone capsule. And the capacitor C10 is used as a shunt capacitor for the high frequency coming from the mixer.
The metal detector circuit is powered by a 9V DC battery or you can use 6 AA batteries for much longer working times. The capacitors C8 and C9 work as a filter. The search coil requires special precision and attention in its construction.
It should be wound on a plastic tube with an external diameter of 20cm.
The coil should contain 100 turns of 0.3mm wire. When the winding of the coil is completed, it should be wrapped in aluminum foil to create an electrostatic shield (this will reduce the effect of the capacitance between the coil and ground). It is important not to allow electrical contact between the winding wire and the foil. The aluminum foil itself should be protected from physical damage, so it should be wounded well with an insulating tape.
Then you should secure the coil in a water proof hard casing, to protect it from damaging it and to get wet.
The diameter of the coil can be different than 20cm. But the smaller the coil, the more sensitive the circuit becomes, but the area of searching for hidden metal objects narrows.
When the diameter of the coil is increased, the same effect is reversed.
Having located the search coil close to the ground surface, adjust the detector with the potentiometer. And so that in the speaker capsule the sound is almost none. Now you are ready to use it and search. If a metallic object will be in the range of the coil the sound will get loud.
Update: Missing resistor value R = 150KΩ.