Begin considering potential postdocs early, while you're working on your dissertation. Finding a postdoc is much more informal than applying to graduate school. Networking is an important way of learning about postdoctoral opportunities. While some positions are advertised in professional newsletters and websites, others are advertised by word-of-mouth, which is why good networking skills are essential to finding the postdoc that suits your needs. Remember that many postdocs open up late in the year, so network throughout the year. Sometimes unexpected funding or a postdoc taking another position can lead to new postdoc opportunities.
When you've found a potential position, thoroughly investigate it. Will it fit your goals? Will you get the mentoring and training that you need? Are current postdocs satisfied? Consider the scientist with whom you will work. Do you respect his or her research? Do you feel comfortable working within his or her research program? Can you interact easily with him or her? How well established is the scientist? Like graduate school, postdocs can open doors to career opportunities. Seek a scientist who is skilled and respected by other scientists and you will not only learn but establish a reputation of your own.