The original schematic is just way too big to fit here. Please click on the upper picture for a full-sized image.
A reasonably effective bfo (bifilar oscillator). Its performance is not comparable to more advanced commercial products, of course, but it still works. Anyway, during WWII metal detectors based on the same principle were utilized my combat engineers of many armies to clear mines.
The main idea is really quite simple: build two identical oscillators and adjust them to the same frequency. One of the oscillators uses the search coil while the second one incorporates a variable inductor. When both are operating at the same frequency, the output is zero. If the search coil moves near any metal, however, frequency of the first oscillator shifts and an audible tone is heard in the headphones.
Theoretically, this principle works well. In reality, though, it has many weak points. Most home-brew devices of this kind will only detect comparatively large metal objects at a short distance. Mine will "spot" a small 5VA transformer at some 15cm or perhaps a little more. Coins and other small objects are much harder to find.
The search coil is around 20cm in diameter and has 20 to 30 turns. Experiment with the variable inductor to get zero output. Construction of the audio amplifier stage is less critical, though. All the transistors used are BC183, but you can substitute them with other amplifier NPNs.
Even though there is a PCB available at the original site, I assembled the circuit on perf board. Wind the search coil on a plastic disk of suitable diameter. Use a sturdy plastic pipe for the handle and place the circuit inside a small plastic at the top of it. Try to imitate commercial metal detectors, they tend to be pretty ergonomically made these days.
A lot depends on proper construction and quality components. Try to make both oscillators truly identical, the only exception being the inductors.
This is really obvious, no need for me to write a whole article on this. An interesting and unusual application, though, would be a metal-activated alarm or garage parking aid for the car.