Steinn gives some advice...addressed to budding astrophysicists, but it's pretty general.
Two pieces of advice deserve more comment.
Pick an advisor you can get on with. Scientists are often "characters". Way high up on the list of "things you do not want to do" is being stuck with a PhD advisor you do not get along with.
Exactly. "Stuck" with is literal. You'll need letters of reference from this person. You'll need someone to talk you up with others and get you invited to talks, etc. I'm talking years and years after you graduate (and of course there are all the horror stories of advisors' behavior *during* grad school!).
And then there's this:
Introduce yourself to the speaker if possible. Go to lunch or dinner or coffee, or meet formally, if you can. Be nice.
These people will often remember you, they may be your future employers, or friends of your future employer, they are virtually certain to be reviewing a proposal or something of yours eventually.
Again, this needs to be emphasized. You need to know people and people need to know you. The powerful physicists are extremely lazy :) and often have to recommend someone for an invited talk or a job or somesuch. Whom do they pick? Someone they know, someone they like, someone in their "camp" (whatever that means). Notice little emphasis on merit.