When I was admitted to graduate school, I read up on each target professor's research, asked them relevant questions, met some at academic conferences, and made sure each knew I was applying to that graduate program to work directly with them before I sent my application in.

I also made sure I wasn't wasting my time applying to work with professors who were going on sabbatical or not accepting new graduate students.

Of course, this was for a history Ph.D., but I suspect the same advice holds elsewhere.