Obtaining the "ideal" postdoctoral position is an important but tough job. I put ideal in quotes, because applicants have their own criteria for positions that will prepare them for their first professional jobs. This search cannot begin too early, since it mainly involves information gathering. The best advice I've received was: "Do your homework."
The first step is to narrow potential fields. Don't take this decision lightly. If you decide to pursue an academic career, you will work in your field for many years: Make sure you love what you're doing. You should also consider how the postdoctoral program may influence your ability to obtain a private-sector position.
You should avoid choosing a discipline that extends your graduate schoolwork. Even if you know you are not going into academia, continuing your graduate work narrows both your scientific reach and the technical experience key to a private-sector job.
Choosing a completely...