Unlike undergraduate studies where learning takes place in the classroom, graduate education occurs with your academic advisor and her/his laboratory. Therefore, it is critical to find an academic advisor with similar interests, and more importantly, with a mentoring style that suits your learning style. To find a potential advisor, do your homework.
First, what are you interested in? While a Master’s or even Doctoral degree topic does not lock in your future forever, your graduate degree should be related to your career interests. For example, do you want to work on fish, plankton, or water quality? Freshwater or marine systems? Behavior, genetics, or population dynamics? Are you interested in experimental versus field observations versus modeling, big picture processes or very focused mechanistic relationships? Do you have strong quantitative/statistical skills? Do you picture yourself mostly doing field or lab work? Think about this last question; fieldwork may seem glamorous and fun, but it is usually the means to an end rather than the sole focus of a project. Field work allows you to obtain samples from which to acquire data, but it can be very undependable due to the uncertainty of weather and animal distributions; lab projects are generally much more controllable. Even with a field-based project, you must be willing to spend considerable time at the computer doing data entry, analysis, and writing).
The next step is to search for a graduate position. There are two basic strategies: surf professional job sites for advertised openings, or directly contact faculty with whom you may be interested in working. The first strategy has the advantage that you know of a position available with funding (see below), and you know roughly what the project involves. The second strategy may lead you to a faculty member who is just beginning to seek a student but has not yet posted the position, or may result in a graduate position in which you need to be a teaching assistant to acquire your stipend. Keep in mind that graduate projects do not necessarily start in September, even though there may be a deadline for graduate applications (more on that in the next paragraph). If you find a graduate project and the faculty member decides to take you on, you can do the formal application at any time of the year. For example, starting in the spring is often useful because you are able to spend a couple of months getting oriented to the university and the project, then be ready to start straight into field work in the summer.
The alternative strategy, used by professional programs, is to simply apply to a university of your choice, and hope for the best. Each department has some funding for graduate students, usually as teaching assistantships (TA), and they need to evaluate the applicants together so they can award funding to the best applicants (hence the deadline for applications). Faculty will meet, discuss the applications, and determine if anyone wants a student. You could end up with an advisor you have never met, a project that does not particularly interest you, or no project at all – you would be expected to figure out a project once you arrive (and hopefully find one that does not require much money). You will also spend a lot of your time as a TA, rather than working on research. This can be a long (and more impoverished – there is usually no summer TA funding) route to a graduate degree.
If you have found one or more potential graduate mentors, you should contact them by email. Keep the email fairly short, and attach your resume to give the prospective mentor more information and something to keep on file to remember you. Don't send an email unless you have done your homework – you know what the professor does, you are interested in what he or she does, and you can say that in an email. A generic message - "I'm interested in the University of Vermont/your lab – what projects are you working on?" is a sure way to get a rapid rejection.