Here's how I built this circuit. If you wish to make your own, you may need to do things differently depending on what materials you have.

Parts needed:

• Ferrite core. I used a toroid core salvaged from a computer power supply.
• Fine magnet wire. I used 30awg enameled magnet wire for the HV coil
• Thicker magnet wire. I used 24awg enameled magnet wire for the primary and feedback coils
  
• Power transistor. Try to use a transistor that can handle at least 500mA. I try to pick transistors that still have decent gain at 100mA or higher
  
• Fast diode. Although a standard 1N400x diode will work, you will get more performance with a fast diode on the secondary. Make sure the diode can withstand the high voltages generated on the secondary.
  
• Resistors and capacitors. It's best to have a variety of parts on hand so you can see what works best in your circuit.
  

Build Process:

1. Wind the HV coil. I found it easiest to first wrap enough wire on a small stick. You can pass this stick through the toroid core when you wind the coil instead of passing a huge length of wire through each time. The goal is to get as many turns as possible on this winding, so make sure you wind the wire tightly to fit as many turns in as possible. Don't wind the coil completely around the core. There will be a high voltage present on the ends of this coil, and you should keep some distance between the ends to help isolate the HV.
2. Wind the primary coil. Using the thicker magnet wire, wrap about 8 turns around the core. Since the insulation on magnet wire is not perfect I tried to keep the primary coil from physically touching the HV coil. If your core is too small you can't avoid them touching. This was the case for me, so I applied a coating called "Corona Dope" on the HV coil to keep it well insulated.
   
3. Wind the feedback coil. Start winding the feedback coil where you finished the primary coil, and keep the polarity the same. The end of the primary and start of the feedback coil will be connected together so it is convenient to place them next to each other. Wind about 4 turns for the feedback coil.
   
4. Strip the coil wires. There are several methods of stripping magnet wire. I prefer to scrape the enamel insulation off with a sharp knife. Strip off enough insulation from the end of each coil wire so you can plug the coils into a breadboard. I like to solder pin headers to the fine gauge wire ends, otherwise they slip out of a breadboard easily
   
5. Prototype the circuit. Following the schematic, start building the circuit on a breadboard. Put the primary and feedback coils of the toroid in first, they will help hold the toroid in place.
   

At this point you should be able to power up the circuit and check the voltage of the capacitor on the secondary. You could do this with a multimeter but I prefer to use an oscilloscope to get more information. If your circuit has no output or it is very low, the polarity of the secondary could be incorrect. Swap the ends of the coil around on your breadboard and try again. With my circuit I was getting an output of about 40V for 1.5V input. Interesting, but not enough to drive a neon bulb. There are a couple solutions to this. By tuning the circuit I was able to get the output closer to 70V, still not enough but a big improvement. I solved this issue by winding another coil of fine magnet wire on top of the secondary. This gives you two HV coils, which you can wire up in series to get higher output voltage. I recommend insulation between these two HV coils, such as the Corona Dope coating I mentioned before. With the two HV coils and proper tuning I was about to get up to 200V output using 2.8V input. I will describe the tuning process next.