Master's or Ph.D.? Two years or five? Part time or full time, public or private, and how on Earth are you going to pay the thousands (and sometimes tens of thousands) of dollars per year it takes to attend grad school?
All valid questions, and there are no right or wrong answers. It all depends on your goals, interests, financial status and availability. Let's go through the most basic initial decisions involved in pursuing a graduate-level education.
Choosing a Degree
There are a variety of graduate degrees available, including M.D. (medical doctor), J.D. (juris doctor, aka attorney), master's and Ph.D. (Doctor of Philosophy). The degree you choose is determined by your goals and interests. If you're aiming to be a medical doctor or a lawyer, you'll of course go for the M.D. or J.D., respectively. If you're getting into something like social work, counseling, business or elementary or secondary education, or you're looking to bump yourself up a pay grade in your current job, a master's degree is the most common choice. To pursue a career as a college professor or a scientist, a Ph.D. is typically preferred.
Your choice may also be guided by time constraints, since a master's will take two or three years, while a Ph.D. can from five to seven years (or more, depending on whether you're part-time or full-time), and by the amount of effort you want to expend -- a Ph.D. is a more intensive course of study than a master's.
Choosing a School/Program
There are several factors to consider when selecting which schools you'll apply to: location, school reputation, program reputation and faculty.
If you're tied to a specific location because you have kids in school, a spouse with a job or own a home, you'll probably want to look at schools close to home, and possibly online. Commute time and availability of public transit may also be considerations. If you're right out of college with no particular ties to a community, your search can easily be regional, national or international.
School reputation is an obvious factor: You'll want to apply to the best schools you can realistically get into. A degree from a more impressive school will carry more weight in the job market. But the reputation of the school's program (Master of Social Work or Ph.D. in Russian literature, for instance) is even more important. An impressive school may not necessarily have an impressive program in a particular area. It's important to research the program's regional and national reputation and faculty. Faculty is especially important, because you're going to want someone to work closely with (like a mentor) during your time, especially if you're pursuing a Ph.D. Finding a faculty member whose work interests you is a prime consideration.
Once you've made your choices, the heavy lifting begins. Your application packet is going to determine where you get accepted.