Stoves

You need to be able to
use your own stove - know how it works, and any safety aspects to consider (including storage of fuel when using your stove and storage of the stove and fuel when you're not using it)
use general fire precautions - make sure your stove is stable, isn't positioned so you can't get away from it if it catches fire, use a wind-shield if appropriate.
know about other stoves - how they work, safety aspects, advantages and disadvantages of different types of fuel. Make sure to read the instructions on any stove
Different Stoves
Zen stoves has TONS of information - more than you need really, but you could read it through once
Wikipedia does too
Types of Fuel
Gas - e.g. in a Camping Gaz Twister stove
Paraffin - e.g. in a Primus stove
Meths - e.g. in a Trangia stove
Petrol - e.g. in a Coleman multifuel stove
Wood - e.g. in a Yukon firebox
Hexamine - e.g. in an Esbit stove
Some info here