Hello, I would like to receive some suggestions about what you think to be the best important things that should be kept in mind while looking for a postdoc position. I'm not considering (in this question) the opportunities one may have from direct knowledge, e.g. because they were pointed out from your advisor or in any case about positions in some nearby university where you have some contact.
For instance while it is often not written explicitly, for most positions the candidate is expected to have taken personal contacts with one professor that may be interested, and set up a research project together. But this is certainly not the only matter, and I would like to hear some story from who has some experience in this kind of issues, also for what regards things which can vary a lot depending on the country (i did my Master and I am doing Ph.D. in Italy, with a short period in France).
To make the question more focused, i'm mostly interested in the scenario of someone working in pure mathematics (e.g. number theory) making application from Europe to some university in North America, or possibly also in Asia.
(EDITED as suggested by quid, making the question CW, and more focused and about data rather than about advice).