The downside to the most environmentally friendly ways of getting around is that they tend to be on the slow side. Walking, biking and riding trains are great for the planet, but sometimes you need to get around the world quickly- and that often involves crossing oceans. The airline industry is one of the largest contributors to global carbon emissions, but it's possible to fly and do minimal damage to the environment.
First of all, figure out whether it's really necessary to fly. If it's for a business trip, maybe you can make do with a phone call or video conference. If it's for pleasure, consider the element of discovery that a train ride can add to a journey- you'll see a lot more than you do from an airplane. But if you only have one week of vacation and your heart is set on Europe, go with an airline that's as concerned about the environment as you are.