Gasification is simply the process of heating up a burnable fuel (wood, paper, dried manure) and causing the combustible gasses to be released. Here’s a quick video demonstration of the concept at work.
Guy has a bit of a stutter, but this is by far the best example of how easy it is to extract burnable gas from fuel. He’s using a propane burner to heat up the chamber holding the gas, but anything could be used to heat it up. This could be piped into your home for oven/stove, furnace, etc.
Now, to “crack” the gas to be able to use in an engine, takes a bit of a different approach, where the wood is actually burned, and the gasses release are cooled down and filters. This is more like catching your fire place exhaust, cooling it down, and filtering it. It still carries a large amount of fuel.
FEMA has plans for this on the internet. http://www.nrel.gov/docs/legosti/old/3022.pdf
This gentleman has built a very nice version of it, and he explains it well.
One could even power a vehicle like in this next video. Could be useful if gasoline become hard to get.