"Dig green living"
"Dig" here means "to like". It's an informal and I would say outdated way of saying to like something. It was more popular in the past, I think in the 60s and 70s, maybe even earlier. I think the author is using it to be a little humorous.
"Green living" means living in a way that does little damage to the environment (driving a car that uses little gas, using light bulbs that don't use a lot of energy, washing your clothes in cold water, etc.)