It depends on how experienced you are, and what kind of experience you have.
If you are an experienced academic, the ads for entry level jobs in the JOE will mostly only be helpful if you are currently an assistant professor and are looking for a lateral move. Then you can simply apply for the jobs in the usual way.
If you are a more senior academic, then you might want to advertise your availability through your network of senior people who know you and who might be asked who is on the market by their colleagues at other universities. Many more-senior-level positions are not advertised in the JOE, or are included along with junior positions in ads that specify flexibility as to level. You can also indicate to your colleagues elsewhere your availability to give seminars, and your openness to the possibility of moving. Often candidates for these positions will be invited to flyouts --or informal seminars--without interviewing at the AEA meetings, and so JOE ads play a much less important role than for junior positions...
If your experience is outside of academia, you will likely face some difficulty moving back into academia unless you have been publishing academic articles, or unless you are so senior that business schools will be happy to think of you as a professor of practice... I have less advice to give about lateral moves from company to company. But here in Silicon valley, for example, economists who work for tech companies seem quite able to network with those at other companies (and meetings like those run by NABE for example may provide further networking opportunities).