I remember Mother Earth News had several articles back in the day...you know, build your own for a couple of hundred dollars worth of scrap. Now they want to sell you a ready made system that costs several thousand bucks.
I have looked into this. You need shit. Lots of shit. If you try to put vegetable matter straight into a methane digester you get mostly CO2, so much CO2 your gas may barely burn. If you run animal waste, such as shit, spoiled milk, blood, renderings you get lots of methane.
I have up in the attic 2 boxes of Mother Earth News from the 70's I remember there were a bunch of articles (Due to gas shortage) on how to build a car/truck to run on wood gas fumes, how to build an electric car. Don't remember methane bioreactor will have to dig them out and start looking. Not long ago I picked up a Mother Earth News how they have changed and not for the better. Come to think of it I have boxes of Organic Gardening mags in the attic
Some eastern communities are putting their s--- together and making a community methane digester and piping the gas to their collective homes for cooking and heating. Any thing organic will work. Another Asian facility school distill their garbage and make alcohol for the kids to have light to be able to do home work. It's not rocket science, well to some people it is.
Are you thinking of establishing one for yourself, or researching one for a fictional story? here are a few ideas... even a very small scale low tech option: