Graduate training in economics requires much more mathematical sophistication than undergraduate economics does. Multivariable calculus (Math 105), linear algebra (Math 211) and real analysis (Math 301) are essential. Other math, statistics, or computer science courses may also be useful as preparation for certain fields in economics. In general, good grades in Math classes will boost your chances of getting into a top Economics PhD program. To get an idea of what economics research is all about (and to get to know a faculty member well), you should consider writing a senior honors thesis.
Where should you apply? There are several rankings available on the web, and these can give you a rough idea of reputations of various departments. Most departments are stronger in some fields than in others -- talk to a professor in the field you are interested in for more specific suggestions on where to apply.
Stanford Professor Susan Athey has extremely useful tips here.
This table of recent outcomes (not a random sample) gives a rough idea of how competitive the process is.
How to finance a PhD? Graduate programs typically offer financial aid to some of the students they admit. If you are a US citizen or resident, you should also consider applying for outside fellowships from the NSF and Javits. If you are an Asian citizen, you should consider applying for the Japan-IMF scholarship.
Mark Foley at Davidson College hosts a page with these and other useful links here.
Graduate programs look for a high score in the quantitative GRE.
You can find a partial list of Williams graduates who have started Ph.D. programs in economics or related fields in recent years (since about 2005) here.