Cut off the socket end of the extension cord and solder it to your prototyping board. Depending on the board, there may be spots for a power supply. If your board has these, solder them there. Otherwise, solder them in an out-of-the-way spot, like a corner. Make sure that the board is not shorting out at your chosen points with a multimeter.
Add a fuse to the prototyping board on the 'hot' end of your AC power source. This is usually a red or black wire, but depending on your location it can be brown or yellow.
Place the 33 nanofarad capacitor on the neutral end of your AC power source. This serves as the first part of a cascading capacitor bank.
Solder a diode from the capacitor to the fuse, with the cathode (banded) end on the fuse side. At the end, place the 68 nanofarad capacitor.
Continue to add the remaining capacitors according to the schematic, continually flipping the polarity of the diodes between each capacitor. This setup prevents the current from flowing in the wrong direction.
Attach the resistors in series to the end of the capacitor bank. Attach five copper wires at the end of the resistor chain. These wires serve as electrodes for your ionizer.
Test your circuit with a multimeter, making sure that your circuit is not short circuiting, then secure it in the small project box.