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When choosing a college, I found that I had an abundance of resources to help me. Every school in the country sent me brochures, in English class we wrote essays for the applications, I got books and magazines with lots of information about lots of schools, and everyone else around me was making the same decision.

Applying to grad school was a completely different experience. Most of my friends aren't math majors, and even those who are were mostly looking for jobs. I had no clue what a personal statement was. Nobody sent me information until I asked for it (and sometimes not even then), and nowhere on the web could I find a page of helpful tips for applying to grad school. So now I'm trying to correct the last situation. Note that all of this advice is intended for people applying to grad school in math, with the intention of getting a PhD and becoming a professor. It may be applicable to others, but I make no guarantees.

First, how do you decide what schools to apply to, then how do you apply?
Ok, so the letters of acceptance/other have started coming in. Now what? One more thing: Once you've settled on a school, then you have to deal with the fun of finding housing and moving in. Start as early as possible. If you're looking for an apartment in Boston, you want to start your search at least two months before you plan to move in, and even earlier doesn't hurt. There are nice online resources to give you a feel for price ranges, but most listings are taken by the time you read them. I was happy with my apartment, but it took me months of casual searching and two weeks of intense searching to find. The fun never ends...
I hope that somebody finds this advice useful. I'll add more advice as I think of it. If you have any important suggestions that I've missed, then please tell me.