It's sort of an exception that proves the existence of the rule. It is indeed common for second rank school A to hire PhD's from school A. My undergraduate institution (which I'd place in the second rank) did this too. However what doesn't happen with nearly as high a probability is for second rank school A to hire PhDs from second rank school B. They'll hire from Harvard or MIT instead.
Another confounder to watch out for is faculty age. Universities do change over time. When I was in graduate school, there were a number of tenured faculty in the department who would not have been considered as potential hires at that time, but who had been hired 20+ years earlier when there was not such a glut of PhDs, not quite so much emphasis on prestige, and when the university itself was not quite as prestigious as it had become.
Most of those folks have retired by now, though, and most departments I look at are even heavier with PhDs from the Harvard/Stanford/MIT/Chicago/etc. than they used to be.
There was some support for the idea of starting an advice repository for grad students much in the same tradition as the Boring Advice Repository and the Solved Problems Repository started earlier by Qiaochu_Yuan. So here goes.
Please share any advice, boring or otherwise, for succeeding at grad school. I realize that succeeding might mean different things to different people, but I believe most people largely agree with what it means in this context. Feel free to elaborate on what you believe it should mean, if you have views on the subject.
I am a theoretical physics grad student, so I'm personally more interested in advice for mathy disciplines (i.e. physics, math, CS), and I also suspect that there are many grad students from these disciplines on LessWrong; but advice for any discipline is welcome as well.
Advice is welcome from anyone, but please do mention your background for providing the advice so that people can weight the advice accordingly. For example, I would be more be open to listening to advice from someone who has completed a very successful PhD, than from someone who has simply interacted with a lot of grad students but has never been to grad school.
Also, feel free to link to advice from other sources, and maybe quote the most useful parts in what you read. Remember, this is meant to be a repository, so that people can come and find the advice, so don't worry if it seems to be something most people would've already read or known.
Thanks!