I can come up with numerous circuits that can be used to convert dc voltages from a low level to a higher level. One such design would be to use a MOSFET and an appropriate control signal at the gate, so that a relatively high frequency square wave is generated. This can be sent to a transformer, which can convert the voltage level - because the signal is AC - and hence an output voltage is generated on the other side.
I adjust the turns ratio so that a desired output is achieved. Then I use a capacitor for smoothing and obtain a DC output.

But given that I have to design a specific circuit (say to convert a 24 V signal to a 1kV signal) how do I decide on the specifics of the circuit - say the current transconductance of the mosfet, how the inductor would respond to step voltage changes, how the output voltage would appear at the other end of the transformer etc?

1- Why do you convert DC to DC? What is the logic behind it?
2- In every conversion you will loose some power.
3- V= W/A . So you will lose power if you convert low voltage to higher level.

1- Why do you convert DC to DC? What is the logic behind it?
2- In every conversion you will loose some power.
3- V= W/A . So you will lose power if you convert low voltage to higher level.

Sorry, but that question is really silly. The most obvious (and common) reason is that parts of some device require higher voltages than others and the ONLY source of power is low-voltage DC, as in a battery-powered device.

Of course there are losses - that's a given.

But there are MANY common and elegant circuits currently employed in *hundreds* of everyday applications that are far more efficient (less losses) than what's described in the OP. Solid state voltage doublers and tripplers are VERY common and can easily be cascaded (added in series).

But you obviously cannot use a doubler/ tripler or similar circuits with capacitors and diodes for a 24V to 1kV conversion can you?

But you obviously cannot use a doubler/ tripler or similar circuits with capacitors and diodes for a 24V to 1kV conversion can you?

Absolutely. How do suppose a stun gun manages to put out as much as 3 million volts?