How can I build a small DC boost converter, similar to what exists on a flash camera circuit board?
A good place to start understanding and designing a boost converter would be by playing with one of the various online power design tools published by part manufacturers, such as:


Fairchild Semiconductor: Power Supply WebDesigner
Linear Technology: LTPowerCAD
Texas Instruments: WeBench Power Designer, SwitcherPro Design Tool


Many of these tools go as far as providing a schematic, a bill of materials,  performance parametrics and in some cases even design simulation, all for free.

Once you have some idea of what works and what doesn't, why, and how, you would have to start either narrowing your design down to use through-hole parts for the breadboard (not many boost controllers are produced in through-hole packages), or putting together little breakouts for SMD parts. 

For the breakouts, consider using the appropriate Schmartboard SMT to DIP adapters, or less finely engineered, much cheaper and yet usable little DIP adapter PCBs from sites like eBay:

 (from this listing)



Important factors to keep in mind when prototyping on breadboard:


You will not be able to operate at high switching frequencies for the boost convertor, due to the stray capacitances and inductances of a breadboard, contact resistance, and the high effective trace distances a 0.1" pitch breadboard will force upon you.
Efficiency will not be anywhere close to advertised figures for the specific parts you choose for your design.
Decoupling is a huge challenge with a breadboard


Every attempt I have made at breadboarding a boost converter has resulted in frequent random spikes and dips in output.

Often boost controller ICs have specific layout requirements, especially for thermal pads for cooling, and you are probably not going to get anywhere with meeting those requirements with generic DIP adapter PCBs.


Good luck, and do update your question to share how you get along.