This simple BFO metal detector requires only a few of components and an evening's work. The two oscillators are simple Colpitts designs using BJT transistors. The reference oscillator's frequency is approximately 370kHz, slightly tunable with the help of a silicon varactor diode. The outputs of the two oscillators are fed to a mixer made with Q3 and Q4. The signal then goes through a low-pass filter (R13, C13) and a JFET preamp. The LM386 audio amplifier has a gain of 20, more than enough for most headphones. If you need more gain, you can add a 10uF capacitor between pins 1 and 8.
The coil should have 20 turns of 0.65 mm (AWG 22) enameled copper wire wound on a 10 cm (4in.) diameter form. Wrap the completed loop with strips of aluminum foil or copper shield tape, then connect the shield to the ground. Make sure the Faraday shield has a gap at one point, so it does not make a shorted loop. You should mechanically secure the coil to a nonmetallic form to prevent microphonics.
After assembly, connect the headphones and slowly turn P1. The pitch will get lower until it disappears. Continuing to rotate P1 in the same direction will cause the pitch to rise again. The point at which the pitch is the lowest and disappears is called "zero beat". If you cannot get this zero beat frequency for the entire turn of P1 you may have to increase or decrease the value of L2.
Turn P1 close to the zero beat position (a tone of 50Hz-200Hz), then move the search coil near a metallic object. The tone should change, depending on the size and distance of the metal.
Note: this simple circuit will only detect relative large metallic objects at a short distance. Coins and other small objects will be much harder to find! If you want to build a detector with a performance comparable to commercial products, try a PI or VLF design.