As a graduate student, you may be considering a postdoc after graduate school. There are several things to consider, such as your field of interest, geographic location of the labs, and the prestige of the new department and university in your field of interest. You will need to put together a CV and prepare for interviews while trying to figure out what labs you could work in.
To help you find the right fit, I share some do's and don'ts of picking a postdoctoral mentor and lab.
DO network. Go to as many seminars and conferences as possible. Be genuinely interested and polite when asking questions about research or career paths. Ask for contact information and keep in touch. Once you feel you are on schedule to graduate, contact your newly established network and let them know that you are on the hunt for a postdoctoral position. Although I tried sending "cold-call" emails, it didn't really work out for me.
DO start looking for fellowships and potential mentors early. NIH and NSF have several opportunities for postdoctoral fellowships. There are other institutions that offer postdoctoral fellowships that get posted to society job boards, like ASM's Career Connections. Make sure to sign up for their email alerts. The key is to identify potential mentors early.
DO have an "elevator pitch" ready. Most principal investigators (PIs) have a couple of minutes to spare, so prepare a 2- or 3-sentence description of your work that you can present sincerely, enthusiastically, and succinctly.
DO make sure that your new postdoctoral mentor has several years of funding for you. If you secure a fellowship, make sure a mentor is willing to fund you beyond the fellowship because they mostly last two years and it is difficult (but not impossible) to secure a faculty position after just two postdoctoral years, if that is your goal. NIH reporter is a good tool for checking funding history of your potential new mentor.
DO talk to the members of your potential new lab. You will be spending a lot of time with these people. It will be important to understand what the lab culture is like. Talk to as many lab members as possible. A toxic lab environment will only add unnecessary stress to your new position.
DO try to understand your new mentor's leadership skills. At one point, most mentors were bench scientists who now have to manage grants and people. It is crucial to understand how a mentor deals with conflicts, publications, project management, time management, collaborations, competition and work-life balance.
DO make sure that your new mentor has successfully mentored other postdocs into faculty positions or other senior scientist positions in a timely manner. If possible, try to set up informational interviews with these "graduated" postdocs to get a better understanding of your new mentor.
DO have a serious discussion with your new mentor about their expectations for your position. Not all mentors are created equal. It is important to understand how they view a postdoc and what their expectations are. A postdoc position is meant to foster growth, creativity, and eventually independence and is NOT meant to be a technical position. If they expect you to work only on their project with no room for your growth, then it is probably not the right lab for postdoctoral success.
DON'T just focus on the "coolness" of the project that your potential mentor is pitching. It is important to understand the long-term goals of the project, your role in the project, potential publications, grants and potential tangential research that would result from the project.
DO pick labs and lab projects that will most likely result in a publication within your first year. Be realistic and not idealistic. All science is interesting and cool, but cool and high-risk projects that don't produce results quickly become a drain on resources and time. As a postdoc, you won't have that kind of time.
DON'T rely on your mentor to come up with ideas for your research. You will obviously be hired to work on a specific project because of your particular skill set. But it is critical that you come up with your own ideas to work on as side projects. DO talk to your mentor about their openness to your new ideas before you start working on your new ideas. Hopefully these side projects can be preliminary data for new grants/ fellowships that you could write with your new mentor or write for yourself when you secure a faculty position.
Once again - DO network as much as possible. Almost everyone I have worked with has been more than happy to pass my CV along or to help me with some aspect of my career growth. Network, network and network some more! Good luck!