They can do many things. I am a Chemical Engineer, but I do know many environmental engineers who I studied with in college.
Some of them go off and design filtration or sanitation systems for water / wastewater plants. Other's may be concerned with cleaning up a pollution dump site, or monitoring air quality coming out of a manufacturing plant.
With any engineering, there may be a fair amount of desk work, looking over system designs and drawings. As an environmental engineer you would also do a fair amount of field work, perhaps taking samples or visiting a site where you systems are being installed.
If should know that strict environmental engineers tend to be some of the least paid of the engineering disciplines, but this also depends on what industry to get into. You can also study in cross-discipline majors (often Environmental / Civil or Environmental / Chemical).
Also check out the ENE (Environmental Engineering) department at some colleges. Send some emails. Usually the staff is more than happy to answer your questions.
Wikipedia has a good article on environmental engineering.