How to referee an academic paper?
How to be a discussant on a seminar paper?

(HT: Chris Blattman)

Here are some great advice on choosing grad programs via Mankiw and Blattman (not limited to Economics).
Mankiw:

1. Start with the rankings. For some recent rankings of economics departments, click here and here and here. All ranking systems are imperfect, but other things equal, higher is probably better.

2. Talk with the graduate students who are now in the programs you are considering. Are they happy?

3. Don't make a decision based on a single faculty member. He or she may leave or turn out to be not quite as wonderful as you now presume. Look for a department that is strong overall.

4. Don't presume you know your specific research interests and focus just on faculty in that narrow area. Many students change their mind over their first few years of grad school.

5. Is the location of the school a fun place to live? Grad school is a long haul, typically 4 to 6 years, which is a significant fraction of your life. Being a PhD student is hard work, but it should not be a miserable existence.

6. Is the university overall a good place? It is always more fun being part of a great institution. Even if the economics department is perfect, if it is an island in a sea of mediocrity, being there will be less satisfying.

7. Are the undergraduates there good students? At some point as a graduate student, you will (and should) do some teaching, perhaps as a teaching assistant in an undergraduate course. If the undergraduates are an academically strong group, they will be more intellectually engaged and more rewarding to teach.

8. Don't be distressed if you did not get into your top choice. What you do in graduate school (or college) is far more important than where you go. Your personal drive matters more than the ranking of the school you attend.

Update: Readers suggest an additional criterion:

9. Look at the record of recent PhD students. What fraction who start the program complete a PhD? What kinds of jobs do they get upon completion? Are they the kinds of jobs you aspire to? The placement record will give you an indication of the caliber of students who enter the program, the value-added of the program itself, and how well the department sells its students on the job market.

Blattman:

... This (referring to Mankiw) is great advice–especially 1, 3, 4 and 8–though one suspects they encourage students to choose Harvard. (Well… maybe not number 5). I would only add a few thoughts:

10. Look for programs with strengths in your area of interest. Clusters of senior and junior faculty are a good sign.

11. Senior faculty are more likely to stay around than juniors.

12. Ask about research and summer support for independent projects and travel.

13. Ask current grad students about relationships with faculty. Do they mingle outside class and mentor their students, and invite them to the dinners with visiting speakers, or do they forget their names and avoid their glances in the elevator?

Mankiw cites NY Times columnist David Brooks in Career Advice from David Brooks:

One of the best pieces of career advice I ever got is: Interview three people every day. If you try to write about politics without interviewing policy makers, you'll wind up spewing all sorts of nonsense.

And, Mankiw on economists venturing out of their ivory tower:

I wonder how different the economics profession would be if economists were expected to do a year of service outside of academia or, at the very least, if university hiring committees rewarded a year of real-world experience as the equivalent of, say, a couple of academic publications. My conjecture is that the profession would be less creative but more useful.

Greg Mankiw gives his advice:

1. Take as many math and statistics courses as you can stomach.

2. Choose your economics courses from professors who are passionate about the field and care about teaching. Ignore the particular topics covered when choosing courses. All parts of economics can be made interesting, or deadly dull, depending on the instructor.

3. Use your summers to experience economics from different perspectives. Spend one working as a research assistant for a professor, one working in a policy job in government, and one working in the private sector.

4. Read economics for fun in your spare time. To get you started, here is a list of recommended readings.

5. Follow economics news. The best weekly is The Economist. The best daily is the Wall Street Journal.

6. If you are at a research university, attend the economic research seminars at your school about once a week. You may not understand the discussions at first, because they may seem too technical, but you will pick up more than you know, and eventually you'll be giving the seminar yourself.

In addition, he offers a fun and interesting reading list, and also outsources the task of offering Advice for Grad Students to his colleagues.

Some Advice from A Yale Professor:
Chris Blattman's Blog: How to get a PhD *and* save the world