Some bookstores carry literary magazines and journals at their newsstands. Depending upon the bookstore, you may find them shelved in any category from "literature" to "hobby." Some libraries also subscribe to a selection of these journals. If you have access to a university library, start there. Don't be disappointed if you don't see any on the shelves. Some libraries have subscriptions to digital databases that include literary journals.
Still, even if you do find some literary journals locally, you may find the pickings are slim. If you already know what journal you're interested in, your best bet is to contact the publication and order a sample copy or a subscription. If you don't have a title in mind, start browsing websites. The Council of Literary Magazines and Presses (CLMP) features a list of member publications with links at CLMP. And many journals have at least some content online, which can help you decide which titles to order.