Boosting DC voltage is required in many applications, like LCD backlight, powering a 5v device with a battery and many more. This app note from Texas Instruments gives a detailed explanation on how it works and how to calculate all your components based on input/output specifications.
The report includes detailed steady-stage and small-signal analysis of the boost power stage operating in continuous and discontinuous modes. A discussion of power stage component requirements is included.
A standard boost dc/dc converter uses a inductor to store current in one state, and then uses that current to charge the capacitor over the input voltage. In the first state the inductor is tied to the ground, while in the second it is tied to the capacitor and provides additional voltage to charge the capacitor. A combination of a mosfet transistor and a schottky diode provide the switching of states.
The app note covers all the basics, as well as all the math you will need to understand the functionality of this design. There is a component selection section at the end of the article.