How does that work then?

It starts with the gas, Nitrous Oxide (N²O, dinitrogen oxide, not NOS (see footnote)), which consists of 2 parts Nitrogen (an inert gas) and 1 part Oxygen (you know that stuff).
Nitrous is used because it contains a higher concentration of oxygen than the air we breathe and oxygen is needed when you burn anything combustible (take away the oxygen, the fire goes out!).
An engine relies on atmospheric pressure to push air into the cylinder (to fill the vacuum) when the piston moves down . It is difficult to fill the cylinder completely as the engine cycle happens so fast. Forced induction (turbo or supercharger) pushes more air in to fill the cylinder better and, with more fuel, releases more of the engines potential. Adding nitrous merely adds a gas which contains more oxygen than air, thus allowing more fuel to be burnt and to be burnt more efficiently.

There are three things that happen when it is injected into an engine:
1. When the liquid N²O leaves the injector, it 'boils' into the gas form of N²O and carries the extra fuel from the cross-fire injector with it. This 'boiling' effect dramatically cools the air that's being drawn into your engine. Cooling the air charge alone helps your engine performance. Turbo cars have intercoolers to cool the charge, but that is to offset the heat the turbo generates. (This is also why you should take care when adding performance filters, put in the wrong place it can make your performance worse.)

2. When subjected to the pressure and heat generated in the engine cylinder as the piston rises in compression, the N20 breaks down into the base elements. The Nitrogen helps keep the gases cool and improves the spread of the heat generated by the burning process and...

3. The released oxygen combines with the fuel and improves the burning of the fuel, releasing more power.

Easy as pie, cheap as chips and bags of fun! Basically works the same principal as a turbo or supercharger. All they do is force more air (which contains Nitrogen and Oxygen) plus fuel into the engine to increase the cylinder charge and improve the burn process. But you try and get a turbo installed for the same price as a nitrous kit!
How long the bottle lasts depends entirely on the amount of boost, bottle size and how long you keep your foot planted in the carpet for!
Nitrous oxide injection is unique in that you only use it when you need it. A tuned cam and oversize carbs are great, but makes driving crap round town. Nitrous is only injected when you are at full throttle and you would only usually use the boost for 10 or twenty seconds a time (but you can run until the bottle or road runs out!), so it lasts a while. That's another good reason to start at a 25hp boost as with anything new, it's hard to stop playing and it's great fun!
25hp boost might not sound a lot, but on an average car it can be a 25% power increase. It certainly makes you car accelerate noticeably better and upgrading to a 50hp shot (or more) is a ten minute jet change that will cost you £12. All WON kits are upgradeable at any time to more power, larger bottles, bottle heaters, controllers etc. We have a bottle upgrade plan that means you could upgrade to an 11lb bottle for less than £57, even after your kit is installed.
footnote: Not 'NOS', that's an American made system and I'll tell you more on them later.