There is no one answer to this question. Why? There are many ways to attend graduate school - and many graduate programs with differing cultures and rules. Take the graduate program that I attended: Working was frowned upon and sometimes forbidden. It was a full time doctoral program and students were expected to treat their graduate studies as a full time job. Students who held outside jobs were few and far between -- and they rarely spoke of them, at least not to faculty. Students who were funded by faculty grants or institutional funds were not permitted to work outside of the institution. However, not all graduate programs look at student employment in the same way.
Full Time Graduate Programs
Students who attend full time graduate programs, especially doctoral programs, generally are expected to treat their studies as a full time job. Some programs expressly forbid students from working while others simply frown on it. Some students find that working an outside job is not a choice - they cannot make ends meet without the cash. Such students should keep their employment activities to themselves as much as possible as well as choose jobs that will not interfere with their studies.
Part-Time Graduate Programs
These programs are not designed to take up all of students' time - although students often find that part-time graduate study takes a lot more time than they anticipated. Most students enrolled in part-time graduate programs work, at least part-time, and many work full time. Recognize that programs labeled "part-time" still require a great deal of work. Most schools tell students to expect to work about 2 hours out-of-class for every hour in class. That means every 3 hour class will require at least 6 hours of preparation time. Courses vary - some might require less time, but those with heavy reading assignments, homework problem sets, or lengthy papers may require more time. Working often isn’t an option, so at least begin each semester with open eyes and realistic expectations.
Evening Graduate Programs
Most evening graduate programs are part-time programs and all the comments above apply. Graduate students who enroll in evening programs usually work full time. Business schools often have evening MBA programs designed for adults who are already employed and want to advance their careers. Evening programs schedule classes at times that are convenient for students who work, but they aren't any easier or lighter in load than other graduate programs.
Online Graduate Programs
Online graduate programs are deceptive in the sense that there rarely is any set class time. Instead students work on their own, submitting their assignments every week or so. The lack of meeting times can trick students into feeling as if they have all the time in the world. They don't. Instead students who enroll in online graduate study have to be diligent about their use of time - perhaps more so than students in brick-and-mortar programs because they can attend graduate school without ever leaving their home. Online students face similar reading, homework, and paper assignments as other students, but they also must set aside time to participate in class online, which may require that they read dozens or even hundreds of student posts as well as compose and post their own responses.
Whether you work as a graduate student depends on your finances, but also on the type of graduate program you attend. Recognize that if you are awarded funding, such as scholarships or assistantships, you might be expected to refrain from outside employment.