My undergraduate advisor told me, "Never do a PhD if you could be happy doing anything else." It was good advice, not because PhD programs are terrible, but because there are many good jobs available with a bachelor's or master's degree.
This issue of the AEA's CSWEP newsletter presents important, up-to-date information on the PhD admissions process in economics. Among the covered topics are pre-doctoral positions.
Before you apply, I recommend you read David Colander's book The Making of an Economist, Redux. Based on surveys of and interviews with economics graduate students, it gives a realistic year-by-year picture of economics graduate school. In my view it slightly overemphasizes the nastiness and competition among students; one can avoid much of this by choosing a program with a friendly culture. You can find a shorter Colander article with some of the same material here.
If your research interests are largely in applied microeconomics, you might consider PhD programs in public policy. Chicago's Harris School and Harvard's Kennedy School have strong programs.
The prominent economist Susan Athey has written up her graduate school advice.
Many graduate schools use GRE math scores, number of math courses, and math grades to make first-round cuts of their application pool. You need to be strong on these dimensions before other elements of your application will receive proper attention. For the GRE, aim for at least a 165 in math.
Williams-specific: some programs do not consider Applied Real Analysis an acceptable substitute for Real Analysis. If in doubt, take the latter.
Once you get past the initial screening, recommendation letters matter more than any other element of your application. If you are seriously considering graduate school, you should spend at least one semester (or summer) as an economics research assistant.
Following graduation, working as a research assistant to a top economist can substantially improve your probability of admission to the best graduate programs. Such jobs are usually advertised through informal faculty networks and web sites for the relevant universities and research labs. Sometimes they are called "pre-doctoral fellowships" or something similar. The Econ RA Listings Twitter feed is a good aggregator.
If you lack some of the required preparation or aren't sure whether graduate school is for you, consider an entry-level research job (e.g. places like this). You can build skills, perhaps take a class on the side, and observe the work done by economists. Ask yourself whether you would be happy doing what they do every day.
For students from underrepresented backgrounds, pre-doctoral bridge programs are another option. These are typically two years, including both mathematics and research experience. I am aware of such programs at Yale, Columbia, the University of Virginia, and the University of Pittsburgh, but there are surely others.
Investigate the placement records of programs to which you are admitted, and assess your career prospects realistically. Would you be happy with the median placement? RePEC ranks programs by student research success here.
RePEC's rankings of "Top institutions by field" (follow the link, then scroll down a lot) provide some guidance on which departments might match your interests. There is noise in these rankings, and sometimes they lag behind a department's current strengths.
Choose a department with at least two plausible advisors, in case one leaves. Junior faculty are fine as committee members but your primary advisor (committee chair) should be tenured (associate or full professor).
Before submitting a paper, compare it to a paper on a similar topic (or using a similar research design) in a good general-interest journal. Your paper should look broadly similar. It should use up-to-date methods. If you have to make excuses for your manuscript, it isn't ready.
Subscribe to NBER working papers in fields that interest you. Even as an undergraduate you will be able to understand the main points of many papers.
If you are interested in labor economics or more generally in applied microeconomics, I recommend the IZA Discussion Papers series. IZA also issues policy papers and other reports that may be of interest.