How does a writer find publications to submit their work to? The answer doesn't seem to be clear cut. I am not well informed, but here are some of my notes on how to go about the search. (This information is heavily biased to the American literary market, but maybe you can find analogues to these sources in your own country.)
Directories and Trade Magazines
In the old days, from what I gather, writers would refer to directories like Writer's Market (WM)  and Literary Market Place (LMP). These books contain lists of magazines, publishers, and literary agents, as well as information as to the kind of work they're interested in. In On Writing, Stephen King calls Writer's Market "the most valuable of tools for the writer new to the marketplace."  I think this sort of information could also be found in trade magazines like Writer's Digest, Poets & Writers, and Publishers Weekly.
These directories are still published every year to keep them up to date. Many libraries have copies of WM and LMP in their reference section. You may be able to find copies of writing/publishing trade magazines at the library as well.
|||King, Stephen. On Writing: A Memoir of the Craft. Scribner, 2000, ch. 4.|
|||Writer's Market is published by Writer's Digest Books. They have an directories tailored to particular forms, e.g., Poet's Market and Novel and Short Story Writer's Market. They publish Guide to Literary Agents. They happen to also publish the periodical Writer's Digest mentioned above.|
Beyond these print directories, there are some online resources that can be useful.
Poets & Writers maintains a list of literary magazines on their website with thumbnail descriptions and genre tags.
The Council of Literary Magazines and Presses (CMLP) compiles a directory of independent literary publishers. While it used to be published in print, it is now available online.
Who Pays Writers is a crowd-sourced database of rates paid by magazines for work.
I think the submission manager Submittable has a "Discover" feature on their website which shows open calls for submissions.
A few times a year, Entropy publishes links to magazines with calls for submissions.
Appendix: How to Submit
Here is a super-short guide on how to submit work to a book publisher or magazine.
If you found the press or magazine in one of those print directories, there are probably instructions provided about how to submit.
If you find them online, go to their website. Look around for a link to an "About" or "Submissions" page. Sometimes these links are buried down at the bottom of the page. There, you can usually find submission guidelines or information on who to ask about submitting work.
Whatever the instructions say—how to send your work, who to send it to, file formats, length restrictions, etc.—follow them as closely as you can. If you know the name of the editor, address them by name in your cover letter. (I won't get into cover letters... I don't know how to write these properly.)
After you've sent your work out, wait patiently. Forget about it. If your work is accepted, congratulations! If you receive a boilerplate rejection notice, don't send any reply. Don't dwell on the rejection, just move on to your next submission. If you receive a personalized rejection, congratulations! Send a thank-you note.