The steps for applying to PostDoc positions
You can also try to approach the best professors in your field and ask them to visit their lab (and most probably they will ask you to make a talk where you present your PhD). It is a hasle to prepare a talk in a prestigious lab, but then you let yourself known, and when a position comes up there you might learn about it first and who knows. 
I would try to contact people I would really want to work with and see what comes next.