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It's a simple bridge rectifier circuit consisting of four diodes and an electrolytic (polarised) capacitor for storing the energy/electricity.

From memory so forgive me if I'm a little off so best to do an image search for bridge rectifiers and look into it yourself.

The older types of what I think you call 'wall warts' also use them as the internal transformer converts your domestic 110V AC supply to say 14.8V AC (approx) and then that goes through the bridge rectifier circuit that converts the AC to around 12VDC current. Each diode has a voltage drop (consumption) of approx 0.6V so it's 14.8V AC minus (4 x 0.6V) = 12.2V DC unregulated output.

Diodes can be thought of as one-way valves that require voltage to operate ~ 0.6V approx. Some types consume more and some like Schottky diodes consume much less.

The electrolytic caps in these are usually 1000uF/25V or 470uF/25V. Why 25V? It's a 2X safety margin. Always go high. The DC waveform straight from the diodes is very rough and the capacitor acts as a reservoir to first store then release the electricity more smoothly. Successive caps can be added to further smooth the waveform - 1000uF-470uF-100uF-10uF-0.1uf. It all depends on how smooth it needs to be for whatever it's powering.

There are much more energy efficient methods used today - voltage regulators, buck/boost units with PWM etc,

If you're thinking of building one to experiment with then it may be best to use the (all in one) Schottky bridge rectifier package. One neat package with low voltage drop internal diodes. You could even mount it to the aluminium plate using some thermal grease or a thermal rubber pad to transfer any heat from the rectifier to the plate.

Note: Electrolytic caps are polarised and therefore need to be attached the right way around. The Negative (shorter) connection is clearly marked. Get it wrong and they'll let the 'Magic smoke' out before going BANG!

Been there, done that. Got the T-Shirt.

Also look up Leyden jars but beware as they can kill from accumulated static electricity.

Interesting to think that the Ark of the Covenant was/is I believe one giant Leyden Jar/Capacitor that would self discharge between the winged Cherubim or kill anyone foolish enough to touch it beforehand. Hence the wooden carrying poles.

Also the tabernacle it was housed in was designed to create static electricity not only to charge it but to power/prolong its self discharge. Very impressive! Very deadly!