Go native. Native plants are used to the climate and don't need extra watering or extreme amounts of care like some non-native plants. In general since there is a natural balance already established in the wild damage from any possible escape from cultivation by seed dispersalis minimal.
Reuse materials. If something can be used again in another way or washed and reused it prevents it from going to the landfill. Things like plastic nursery pots, yogurt cups(see my heuchera seedlings for that one), and old lumber can always be reused. Some nurseries collect their old pots for reuse so check with them when you buy your plants if you don't want to reuse them for yourself.

Efficiently utilize water. Drought issues have been very common for us here in the Southeast over the last couple years. It just underlines the importance of good water management. When we water we should water deep to encourage the roots to follow the water. The roots will still follow the water if you water shallow but the problems but they won't grow deep. They will become shallow and will stay in the first couple inches of the soil. The deeper roots can get to the moist ground underneath which allows the plants to become more drought tolerant. Watering deeper means you will have to water less often and you will save water and money in the long run.
Irrigate your garden with soaker hoses or drip lines underneath the mulch to prevent water evaporation. Soaker hoses and drip lines put the water on the ground while sprinklers send it into the air. Once in the air it begins evaporating and much of it is wasted.
Consider installing rain barrels along downspouts to collect water when it rains and utilize it for your plants. You could do what I have done and take a plastic storage tote and drill a bunch of 1/16" hiles in the lid. I leave it out in the garden and rain water gradually collects inside. The small holes won't let mosquitoes in and I have an extra source of water for my vegetables.
Never Throw Away Compost! Compost is the best thing for gardens! If you save your vegetative food scraps and toss them in a pile or compost bin over time they decompose and become the best additive you can find for your garden. Not only is it good for your plants but it keeps unnecessary food waste from entering our landfills.
There's just a few tips for "greening" up your gardening for this St. Patrick's Day. Of course it really doesn't matter what you or I do on March 17th, it matters what we do the rest of the year!
Happy St. Patrick's Day!