Journals provide a miraculously free and civic-spirited service that aims to improve your work – peer review. When you submit a paper to a journal, the editors ought to send it out to at least two peer reviewers (sometimes several – practices differ). They ought to have some specialist knowledge of your subject. If your subject is controversial, one ought to be ‘on your side’, another perhaps hostile or at least neutral.
Ideally, peer-review is ‘double-blind’ – the reviewer doesn’t know your identity, you don’t know theirs. In small specialisms, where everyone knows who their fellow-workers are, this anonymity is difficult to maintain, but it’s an ideal worth preserving, so try (as best you can) to anonymise your own manuscript – don’t refer to other work of yours, or if you do refer to it in the third-person.
You should get reports back within 2-3 months. (Does this seem slow to you? Remember, your referees are doing this as a public service, and they probably have more than full-time jobs, so they will fit such tasks in when time allows. Anyway, what’s the rush? History moves slowly.) They ought to provide feedback not only on whether the paper is publishable, but also on the specific arguments, evidence, style and presentation. With the reports, the editors will deliver a verdict. They might accept or reject your paper outright. More likely, they’ll ask you to ‘revise and resubmit’.
A good editor will steer you towards specific comments in the referees’ reports that you ought to take into account when revising. (If they don’t, and the reports are contradictory, ask for a steer.) Take as much or as little time to revise as you like – the ball is in your court. Sometimes editors will send your paper back without peer review. This will normally be because they think it unsuitable for the journal. Try another journal.
For more details on what and how to submit, and where, see submitting to a journal.