I have a nice and (I think) significant result. I would like to publish it, but I have no idea how. It's a proof of an optimal institutional structure. Who do I contact?
If your paper is rigorous enough, you might want to submit it to a peer-reviewed specialized journal. Journals pertaining to Economics are the Quarterly Journal of Economics, Journal of Macroeconomics, The Economic Journal, and many others. Many of these journals have a link for writers to submit their paper and a "guide for authors". Likewise, search on Google for Call For Papers.
The question by @MichaelGreinecker (whether you know anyone in the field) makes me wonder whether being accepted for publication also depends on having connections with the editorial, rather than being exclusively a matter of rigor of the research.