DC to AC converter circuit
An electrical transformer is basically two coils of wire that are closely wound with each other but not electrically connected. These are used for converting AC power voltages to low voltage AC voltages such as in wall-warts. However, transformers can be reversed to convert a much smaller AC voltage into a much larger AC voltage. A good example is the ignition system on a petrol car. 12Vdc is the battery and voltages of around 10,000 volts can be produced.

In other words, the transformer is the key element in making a high voltage output from a small battery voltage. You can easily generate many thousands of volts from a 1.5V battery. You can add a rectifier and smoothing capacitor and you get a clean and relatively stable high voltage DC of (say) 10,000 volts from a 1.5 volt battery.

It is do-able but you also have to remember that power-out equals power-in minus losses. A switching circuit that can power a transformer from a 1.5V battery may be only ~70% efficient. This has to be borne in mind. Also, if you were generating 10,000 volts and the load on the output were 1mA i.e. a 10 M-ohm load, the power out would be 10W and the current taken from a 1.5V battery would be nearly 7A. Obviously, this is unsustainable for an AA-size battery and this becomes the biggest issue in generating high voltages from really small DC voltages.