Disclaimer: These are just opinions, and some people may disagree with the claims here. You should seek opinions from your advisors.
Choosing classes
Graduate schools care much more about what hard classes you've taken and how you've done in them than about overall GPA.
If you have taken difficult classes its probably a good idea to point this out in your application essay because schools might not know what the math classes are, which economics classes are the advanced ones, etc.
Real analysis is an especially important class because it tends to be demanding everywhere, and forces you to do logical and formal proofs. Get a good grade in this class.
Taking some graduate classes can be a good thing, but be prepared. You will be at a disadvantage since the grad students will all have study groups. Try to join a study group and devote serious time to any graduate classes you take.
Recommendation letters
Recommendations which are not from economists have very little value. Recommendations from economists who have contacts at the schools you are applying to are most useful.
Get recommendations from people who know you well.
Corollary: Get to know some professors well. Professors will be very excited that you want to get a Ph.D. in economics. Don't be afraid to approach them. Listen to their advice.
Give professors every possible opportunity to say they don't feel comfortable recommending you to the school you're applying to. If they express any hesitation don't have them send it. One bad letter hurts much more than any good letters can help.
It's fine to have a letter from someone you worked for even if they didn't teach you in a class.
Application Essays
On your graduate school application its very important to write an essay saying what kinds of areas of economics you're interested in, what questions you think are interesting, what papers you've read that you've liked etc. Be as specific as possible. It may be helpful to discuss your thesis or research assistant work. Its not necessary to have a specific thesis proposal, and odds are if you try to pretend you have one when you really don't you'll come off as sounding naive which is a bad thing. Mostly schools just read these to see what field you're interested in and to get a sense whether you have any idea what you're getting yourself into. You should therefore try to talk intelligently about your topic of interest to show that you understand something about what research in that field would be like.
Get someone to read your essays, preferably an advanced graduate student or a faculty member.
Application essays for NSF fellowships have typically been judged differently. They seem to want a specific thesis proposal and value clear brief surveys of the existing literature, a clear statement of what you'd like to add to this, a discussion of datasets you might want to use etc. They don't like vague statements about liking economics, and don't seem to mind that people aren't really going to do what they say.
NSF Fellowships
Every student applying to graduate school should apply for an NSF fellowship. Winning one gives you a much better financial deal than any school will offer. Even if you don't win just the fact that you applied will increase the probability of your being accepted by graduate schools.
Don't be surprised to find that the fellowships are only weakly influenced by grades and GRE scores. The essays matter a lot.
Even if its questionable whether your eligible go ahead and apply. The rules seem to change a lot.
Apply from your home address if you attend college in states like Massachusetts or California. There is some allocation by home state, since this is a federal program.
Application timing
As long as its in by the deadline it doesn't matter. It is an advantage to have your folder be complete very soon after the deadline, which means making sure your recommenders get their letters in.
GRE Scores
Though the test is not necessarily a good predictor of success, it matters a lot (especially the quantitative portion). Studying for the GRE dramatically increases your scores so you should definitely practice.
The economics GRE doesn't usually count for much, but it does give a chance for people who haven't taken much economics to make a positive impression.
Financial statements
Its hard to generalize on what you should do on these. At Harvard, for example, its always best to make it seem like you have money because their administration has a rule that they can't accept people without offering them enough money to come. As a result they often reject people who at the end of the process they would have preferred to people they give money to. At other schools, if you seem to have a lot of money it may reduce the size of the fellowship offer you get. It may also, however, increase the probability of getting accepted because a school with a few partial fellowships to offer will give them only to people who seem to have the resources to accept them.
Where to Apply
If you are well-qualified, you should apply to all of the top-ranked economics departments (e.g. MIT, Harvard, Stanford, Princeton, Chicago, Yale), and several backup schools, depending on the strength of your record. You should definitely seek advice from faculty members on this.
If you have a somewhat weaker record, there are lots of good graduate programs out there, but you need to shop more carefully for schools that have well-known advisors or have recently been investing a lot in graduate students. Some middle-ranked schools (like recently Pennsylvania State) aggressively recruit prospective students and have placed graduating PhD students in top 5 schools by investing heavily in the students. You need to do a lot of homework, and talk to lots of faculty about good places to apply. Information about good places to go is likely to be dispersed.
Don't overlook the small but prestigious PhD programs at business schools: Stanford GSB has a placement record that rivals the top economics departments, and Harvard and Northwestern also have programs worth looking into. These programs typically offer more individual attention and have more generous funding.
Visits and Contacts at Graduate Schools
With rare exceptions, you SHOULD NOT initiate contact with faculty members at schools you are applying to before the admissions decisions. You will seem like a pest and like someone who doesn't understand the system. After you are admitted there will be plenty of opportunities to meet faculty. If you feel like you have an exceptional case for contacting a faculty member at another school, seek the advice of your advisor first.
After admission you should visit your top choices if at all possible. You will learn an enormous amount then, swamping what you have managed to figure out before then.
Talk to the students to learn how often they meet with their advisors, who is really accessible, and how the morale is among students. Some faculty do a lot of aggressive recruiting but don't spend a lot of time with their students later. The current students can tell you how advising really works.
Anyone who tells you that one department is best for every student is not being very thoughtful. You need to determine whether a department feels right to you, and whether you feel like there are a set of potential advisors for you. Your advisor will have enormous power over your life. You need to be comfortable. Different departments have different strengths, cultures, and styles. Some fields within departments have very strong subcultures and impressive placement records. Learn about those.
Find out about the placement records of the programs. Don't just find out about the top 5 students--find out about how number 10 or 15 in a class did. Even if you are quite certain you will be a star, it's possible you won't be the very best, and even if you are, it will be a lot more fun if your classmates aren't unemployed, despondent and neglected.
