Start by looking up a journal or publisher in the resources listed below.
A particular publishing peril in recent years is the advent of many "open access" journals with publishing fees that purport to have genuine peer review, yet their contents seem to belie that. Besides examining the articles in fields with which one is familiar, how can quality be determined? There are no "hard and fast" rules that allow one to determine whether a journal is of low quality. A "yes" answer to just one question may not be a problem, but affirmative answers to several of the questions below may be an indicator. Examine the journal's and/or publisher's Web site with these questions in mind.
Is the journal's subject coverage broad and vague? Journals with the true primary purpose of making money from author fees want to be able to accept as wide a variety of papers as possible, so they may have titles such as "Journal of the Social Sciences and Humanities."
Does the journal publisher list many specialized journal titles, and lots of them? An alternate tactic to broad journals is to have specific subject coverage, but list so many titles (dozens to hundreds), that the maintenance of quality has to be questioned, especially when the publisher was recently established. Some of the listed journals might not have had any issues published.
Are the article reviewers and editorial board members of high reputations in their fields? Be aware that even if they are, they may not actually be affiliated with the journal. This can only be determined through contacting the person listed. Searching for an author in Web of Science (covering sciences, social sciences, and humanities) will let you know how much they have published and how many times they have been cited.
Are there many disparate articles in one issue with little or no organization? This tends to be characteristic of the broad, general subject journals. Wide subject coverage; no organization into "case studies," "research notes," etc.; no manuscript history information -- all may be indicators of low quality.
Are there repeat lead authors, sometimes in the same issue? Certain authors, especially in the sciences, are prolific. But multiple articles with the same author leading, or as sole author, published within a year or so in the same open access journal may be cause for question.
Is the journal indexed in multiple selective databases by different publishers? This is something that can be looked up in Ulrich's, and should not be accepted as true based on what the publisher says. Indexing in one database does not guarantee quality. Although journals cannot pay to get indexed in databases, sometimes database publishers slip up and let lower quality journals into their list.
Does anything come up if you search the Internet for "publisher name" scam or "publisher name" fraud? Others may have already found a particular journal or publisher questionable.
Jeffrey Beall, who has pioneered in guarding against predatory open-access publishing, has a more extensive list of criteria.