I just graduated with my PhD a few weeks ago and have been spending some time thinking over my grad school experience. In the coming weeks, I'm sure I have a lot to say about choosing a grad school, a research field, an advisor, etc, but I thought I'd start by talking about the most important things I learned during the journey. Here goes:
(1) Follow all your leads and persevere: The most important piece of advice I've got. Most projects will not go smoothly, either because of lack of data, some weird programming bug, or some other unforeseen difficulty. If you think it's a good project, with your intuition screaming "yes" and you sense that a breakthrough is possible, KEEP GOING. Sometimes you need to hit your head against the wall, over and over, till it breaks down. I was in this position about seven months ago, needing a third paper for my dissertation and not sure if I was going to get it to work in time to graduate by May. I found some interesting preliminary results on the long-run effects of clean water and I decided to go forward, working really hard to get data and program what turned about to be conceptually easy, but difficult in practice. It paid off, and I am hoping to expand this paper over the next year in several ways.
As far as the "following all your leads" part, if you think of an interesting question, find some data (it's usually very cheap!) and spend an hour or two seeing if you can't get some preliminary evidence or "proof of concept." If you do, follow it up: the results may surprise you and might have an interesting project on your hands.
(2) But know when to stop: This applies to two situations. The first is with a project that just won't work out anytime soon. And the second is with a mostly complete project. In both situations, the marginal hour, or tweak here and there, will likely not lead anywhere. In the first case, stop, but always keep it in your mind: you're breakthrough could happen a few years later. In the latter case, send the thing out already!
Of course, while you're in the thick of it it's hard to distinguish between when you should take route (1) or (2) [I've been late to pull the trigger on several occasions!]. I think that's part of what graduate school gives you, an intuition of when things will work and when they won't. Until you get there, the best way to distinguish between (1) and (2) is to outsource the experience and intuition based calls to people who have a comparative advantage in these things: your advisors.
(3) Sell, sell, sell!: This is something I really picked up in the last six months of grad school. How well your paper does or how well your talk is received is really based on (a) whether your intended audience gets what you are saying and (b) how well you couch your work in the larger scheme of things. Basically, people need to understand what you are doing and realize that it is important. The only way to get this is with a nice sales job.
For people in fields that are necessarily interdisciplinary (health economics or health service researchers both fit that bill), you need to be able to communicate to people who look at problems with a different disciplinary lens. I noticed that my talks went a lot better when I cut out the economics jargon and explained things in a more universal language. My writing got better from this, as well.
In motivating talks and papers, it is always important to bring in the larger literature first, show where your study is situated, and, at multiple junctures, point out exactly why your study is important and all the new stuff it adds to our knowledge. Humility is good, I've learned, but too much gets you left behind. (On the same plane, too much boasting is bad, too. Never oversell your paper!)
(4) Get really good at fundamentals: My personal view is that it is a lot easier to learn about different topics than it is to pick up different skills. As such, I think the best investment during your graduate years, especially when you are taking classes, is to invest in skills. In any statistics based field, being a quant jock makes you the cool kid at school: everyone will want to work with you.
This doesn't mean that one shouldn't read up on interesting topics. Far from it (see below)! Just make sure you get the requisite tools.
(5) Always work the margins: Grad school is full of ups and downs. On the research side, you'll go from being uber productive to not so productive and back again. I think its really important to have a strategy of riding out low marginal productivity months. This might be the time that you (a) read a lot (b) write a lot (c) take a vacation. Whatever you do, make sure you do it with relish. At some point you will become productive again and have a storm of ideas. When you do, embrace it and go to town.
Some other nuggets of note:
(6) Keep a notebook or pda with a list and short description of all your ideas: Some of them won't pan out initially, but you might be able to revisit them in the future.
(7) Read the popular press: Two of my working papers have come from taking data to statements and problems outlined in newspaper/magazine articles.
(8) Read the literature, but don't binge on it: Some good advice that I got early in grad school was to know the literature, but don't read so much that it destroys your creativity. If you think of an interesting idea, play with it in your mind and ask yourself how you'd address the research question. Once you do, Google Scholar it and see if its been done. If it has, pat yourself on the back for coming up with an interesting question and do it again if the authors adopted your methodology. If not, go to town.