Undergraduate students seeking a masters degree in environmental policy should have already had some experience with the history of environmental policy and modern iterations. Understanding that work in policy can be frustrating, and being ready to see politics mold legislation is important as well. If you are still focused and committed, then the arduous study and learning will be made easier. Most graduate programs take 2 years to complete, so be ready for a long term commitment. In those 2 years, much of your study will be directed at developing a thesis, which is to be the focus and pinnacle of your masters education, and demonstrate that you are a qualified expert in your field.
Masters programs are not as formulaic as many undergrad degrees can be. In a masters program you will work with advisors to develop your thesis work, performing a lot of individual research and refinement. In a field such as environmental policy, there are countless possibilities for a thesis focus. Opportunities may be limited by a school's individual staff and programs, but some examples would include analysis of specific policies and legislation like the historical effectiveness of the Clean Air and Clean Water acts, current impact of ISO 140001, or drafting of future policies to deal with climate change and emerging environmental contaminants. In addition to taking classes to fuel their thesis knowledge, most graduate students will spend some time as teaching assistants for undergraduate classes.
Holding a masters degree amplifies career and further education opportunities for an field of study, but with a contemporary shift towards environmental consciousness, an MA or MS in Environmental Policy is particularly advantageous. Policy analysts are in increasing demand, but work in the private sector is also viable. As more companies adapt "green" policies and standards, corporate leadership seeks skilled and knowledgeable individuals in environmental policy who are able to sift through the rigors and challenges of drafting sound policy, and produce something that will hold up to federal environmental standards.
In addition to career opportunities, earning a masters degree is also a step along the journey to a doctorate degree, or other academic fields. University positions are difficult to get without at least a masters degree, and often times a PhD is necessary for more accredited positions. However far you go, earning a masters degree in environmental policy is a major step in an academic career.
The best way to make sure you are applying to a university that fits you is to go and visit, and talk with advisors or other graduate students. Advisors and faculty from your undergraduate university are likely to be very helpful in your search for a graduate program, but don't be surprised if they suggest their Alma Matter.