Wood stove fans cover two main categories - those for boosting draft to the firebox and those designed to increase air circulation around your fire, and hence heat flow into the room.. I'm not planning on talking about those that feed combustion air to fireboxes directly here, although I may cover them in a future article.
Under normal circumstances the air circulation in your home may look something like this

Wood stove fans boost stove heating efficiency by improving the amount of heat that your stove can transfer to the air in your room, and also how that heat circulates around your house. Some houses have in built ducting to carry air from one section of the house to another - I don't have experience of these systems as they are not at all common in the UK, although I am led to believe that they are common in the US.
If you are lucky enough to have one of these systems then it can probably be controlled to circulate the air around your home moving heat from the hottest part of the house, where your wood stove is, to the coolest.
This forced circulation helps by spreading the energy from the stove to the farthest flung corners of your home - this stops the space with the stove overheating and reduces the need for additional heating in other parts of the house.

If you don't have a system built into your home it is unlikely that you will be thinking of building one - in that case you may find that giving the natural circulation of warm air within your home a helping hand will bring handsome benefits.
First, a few counterintuitive things about air circulation:
The wood stove fans we have made, and I have to credit my father here for the creation of this masterpiece, are made from a couple of pieces of scrap wood, an old mobile phone charger and cooling fan salvaged from a PC! Talk about a cheap heating solution!
These simple little devices are small, portable and plug into an ordinary power socket - simply placing them on the floor in strategic places has a noticable impact on how warm distant rooms get. When not in use they get put away in a drawer.
They won't be everyone's cup of tea as they look 'homemade' but they are a simpler solution than cutting holes in walls to install heat ducting!
Here are a few ideas for places to try putting a fan - remember we are simply trying to encourage the natural convection not force air where it doesn't 'want' to go.
The Eco-Fan is another new piece of technology that has recently hit the market. These come in various styles but rely on the same technology for the power supply. The fan sits on the hot surface where alternating metalic strips generate a voltage and some current. This is enough to power the fan unit, which is optimised for transfering a large volume of air.
These are relatively expensive at present.