1. Find someone, anyone, at your new institution and start working on their problems. It will help you broaden your horizons and get over some hurdles of being a newbie again. We all like the warm comfy feeling of working on what we know so it takes some courage to start in a whole new direction. Clearly, it is easier to try it as a postdoc when you have experts around than if you try it on your own as a new professor at a small college where you are the only one in your field. Furthermore, you will need a letter of recommendation down the road from someone at your new institution.
2. If there are other postdocs around, start a postdoc seminar. Just send an email around to all the postdocs asking them to get together and discuss the idea. If they are willing, have each person give a talk on their research but aimed at a broad audience so you can all understand. People like hearing math they can understand. Plus you will all learn something. Karen Smith did this at MIT while I was postdocing there and I am incredibly grateful to her for her inspiration. The other postdocs at the time were/are some of my dear friends and a very useful network of mathematicians.
3. Join a club or a church or a choir or a sports team or something to meet people outside your department. Diversity is a good thing. It has just as much to teach us as our main focus of study.
4. Work hard. I would have put this first, but I assumed it obvious. What does work hard mean? In math it means do at least 4 hours of research each day. Go to all of the seminars in your field and the ones that are closely related to your field. Take every invitation to speak. Write up your work clearly and carefully and submit it promptly for publication. Tell people open problems you have though about and see if they have any insight or interest in collaborating. Create useful tools and share them on your website. Scan the math arxiv every day. Keep a research journal. See my advice to grad student on my website because all the good habits developed there should be continued.