You can start by eliminating meat at least once per week; find useful recipes on meatlessmonday.com. You can also take the flexitarian approach by eating some vegetarian meals and making meat less central to your meal.
In the article “The Triple Whopper Environmental Impact of Global Meat Production,” Bryan Walsh, gives more details describing the impact of livestock on greenhouse gas emissions (Science.time.com, Dec. 16, 2013)
http://science.time.com/2013/12/16/the-triple-whopper-environmental-impact-of-global-meat-production/