You have written a scholarly article, now what?
Now it's time to get published, and you need a publishing strategy.
First, you should upload your article as a working paper to the Social Science Research Network (SSRN). This is free and is keyed into Google search results. Many preemption checks require would-be authors to search SSRN for working papers on their topic, so uploading to SSRN lets others know that your article exists and will (hopefully) be published soon. Additionally, SSRN tallies article downloads, so if your article is downloaded many times on SSRN, you could use that information in your cover letter to a law review or journal as a reason why the journal should publish your article.
Next, you should start an ExpressO account and Scholastica account. ExpressO & Scholastica are electronic database that most law reviews and journals use to receive article submissions. They are propriety databases (i.e., for cost), but, if you are a student, you can sign up and receive one free submission. In addition to your article, you will need a cover letter, an updated CV, and an abstract. Each of these items can make a difference when trying to get published.
You might decide to submit to a variety of law reviews or journals -- both general interest and special interest. All of the 200+ law schools in the U.S. have a flagship law review that is considered general interest, but there are many more special interest journals that focus on a particular area of law. Many authors decide where to submit based on the rank of the journal, and Washington & Lee maintains a well regarded law journal rankings database. If you do receive an offer to publish, you could use that offer to negotiate with a higher-ranked journal and ask for an expedited review.
The optimal submission season for most law reviews & journals is mid-August through Labor Day, as most schools are out for the summer, so they will not start reading submissions until this time. If you decide to submit later, you might find that the law review or journal has already filled their issues for the year, or the journal may have chosen an article with a topic similar to yours, and you may get rejected.
Above all, do not fear rejection. There are a variety of reasons why a law review or journal might pass on publishing your article -- many that are outside of your control. But don't give up. If you have an article that is logically strong and formatted properly (including citations), my mantra is "(s)he who works the hardest at getting published will get published."
For more Information for Submitting Articles to Law Reviews & Journals, see this annually updated document by Allen Rostron & Nancy Levit. This document contains information about submitting articles to law reviews and journals, including the methods for submitting an article, any special formatting requirements, how to contact them to request an expedited review, and how to contact them to withdraw an article from consideration. It covers 203 law reviews. The document was updated in July 2016.