From ATTRA, we read: “Anaerobic Digestion works in a two-stage process to decompose organic material (ie, volatile solids) in the absence of oxygen, producing Biogas as a product.

There are several types of anaerobic digesters, the most common being:

• Covered lagoons — a pool of liquid manure topped by a pontoon or other floating cover. Seal plates extend down the sides of the pontoon into the liquid to prevent exposure of the accumulated gas to the atmosphere. Designed to use manure with 2% or less solid content, this type of digester requires high throughput in order for the bacteria to work. Basic components of an Anaerobic Digestion system on enough solids to produce gas. Most frequently used in warmer southern regions, where the atmospheric heat can help maintain digester temperatures, this is the least expensive of all designs to install and operate. About a third of all digesters presently in use are covered lagoon systems.
• Complete mix — a silo-like tank in which the manure is heated and mixed, designed to handle manure with 2–10% solids. This is the most expensive system to install and operate, but it’s particularly appropriate for operations that wash out their manure. Less than a third of all digesters in use are of this type.
• Plug flow — a horizontal or cylindrical tank in which the gas and other by-products are pushed out one end by new manure being fed into the other end. This design handles 11–13% solids and typically employs hot water piping through the tank to maintain the necessary temperature. Most appropriate for livestock operations that remove manure mechanically rather than washing it out, the plug-flow system accounts for more than a third of all digesters presently in use.

There are also a number of hybrid systems being designed and installed, a strong indication that there is no single system right for all or even most situations."

Here are some reference links to get you started: