Methane production from digestion in ruminants
Ruminants include cows, goats and sheep. They produce methane as a by-product of their digestion process.
A ruminant has a stomach with four compartments: the rumen, reticulum, omasum and abomasum.

Digestive system of the dairy cow
Source: J Moran, Tropical dairy farming: Feeding management for small holder dairy farms in the humid tropics, p.42, Landlinks Press, 2005.
Microbial bacteria found in the rumen, called methanogens, convert feed into a product that can be digested by the animal. This process, enteric fermentation, produces methane which is exhaled by the animal.
The amount of methane produced by a ruminant can be likened to the greenhouse gas emissions of a car. In fact methane emissions from the digestion process in ruminant animals comprise 73% of the agriculture sector's greenhouse gas emissions in NSW. Across Australia, ruminant animals alone contribute 13.1% of Australia's total national emissions.1
Research
NSW scientists are working towards ways of reducing methane emissions from the livestock industry - read about this research.
1Hegarty, R (2007) Greenhouse Gas Emissions from the Australian Livestock Sector; Australian Greenhouse Office.