An effective graduate school search will yield several schools to which you plan to apply. It isn't difficult to find "the best" school in a particular discipline, but to protect yourself you are probably also going to apply to several "very good" schools too, so comparing them in meaningful ways, other than using that nebulous thing called "reputation," should be done as systematically as possible.
I recommend that you make a table whose horizontal axis contains the names of each school that you are thinking of applying with the categories that I will provide in this and several subsequent articles listed in the table's vertical axis. Filling in this spreadsheet is hard work. Some of the information you are seeking will be available on a school's web site [though it will take digging to find it] and some will be in the school's hardcopy Peterson's Guide entry. The rest of the information is gathered by calling the schools, contacting a program's graduate chair and probing for facts. Yes, it is time consuming and yes, a call like this will put you on their radar, and yes [and most importantly], they will understand that you are a serious, committed student if you are asking sophisticated questions.
Begin by examining admissions statistics and Graduate Record Examination scores [in cases where the tests are required]; this will help you to see how difficult this school might be for you to get into. Then determine the number of students they accept each year, how many apply, and try to get a fix on the program size [total number of enrolled students]. Unlike college where you took classes across many different departments during four years and got to know different students from different disciplines, in graduate school your personal horizons might be constrained by a small program in a small school. If you come from a large university where you had latitude and lots of friends, a small program might be constricting. Remember, you are joining a family, albeit as a transient member, and whom you know and whom you work with will affect your everyday life in many ways.
The size and diversity of the faculty is another variable you should explore. If the faculty is small and the number of students large, will the faculty have time to provide the individual attention you want as a graduate student? Remember, undergraduate students are also part of a faculty member's advising load. You also want to know if the faculty is strong in the fields that you are interested in in order to be able to provide the supervision you will require on your dissertation. If modern poetry is your passion and there is no name brand scholar at school X who shares that passion, you might take X off of your list.
Requirements are another important factor as you compare schools. You may find some programs too restrictive, or too requirement heavy for your tastes or needs. Perhaps you don't think you need to pass proficiency examinations in two foreign languages and several of the schools you are interested in think you do and several do not...then you should be asking why this discrepancy exists and figuring out which program is best for you.
Finally, the number of graduate level classes offered each year is a very important number. If, as is sometimes the case, the program offers few classes at the graduate level and double counts upper-level undergraduate courses and applies them towards your graduate program, then you will be taking more classes than you expect with seniors or advanced juniors, not with your graduate student peers; or you may have to fill your program with courses you would prefer not to take to maintain full-time status. This would be an especially bad deal in a one-year Master's program. Essentially, you are not quite getting what you came for, even if the instructor provides an extra hour or an extra section for graduate students [and that might not happen either]. So be sure to ask, and if the answer is that there are not many stand-alone graduate courses, try to find out why and determine if this is a deal-killer for you. This question may not make you popular, but ultimately it may make you happy!