A first step you can take to verify the quality of the publisher or journal is to see if the publisher is a member of quality controlling organization or if the journal is indexed in a quality-controlled database. If the publisher or journal is not included in the sources below, it doesn't automatically mean that the publisher or journal is predatory or questionable. What you can do then is to look closer at them from the viewpoint of the control questions presented below.
These two databases have a quality procedure for the journals they index. They are also looking at other aspects which don't deal with the quality aspect but rather with their impact on the research community in the form of citations. This means that there are many journals of quality that are not indexed in the databases. However, if you find the journal in any of these databases you don't necessarily need to go further with the quality control.
Journal Selection Criteria [12:23]
Directory of Open Access Journals - DOAJ
DOAJ indexes open access journals which meet their best practice which, among other things, includes aspects such as peer review, editorial board, contact information, ethical publishing principles, retraction policy etc.
Principles of Transparency and Best Practice in Scholarly Publishing
DOAJ: Journals added and removed
INASP (International Network for the Availability of Scientific Publications) is an "international development charity working with a global network of partners in Africa, Latin America and Asia", for them to gain access to and be able to use information resources to solve the developmental issues at hand. One of the projects of the organization is the development of quality based journal databases. Journals Online contain, as of now, six databases: African Journals Online (AJOL), Bangladesh Journals Online (BanglaJOL), Latin America Journals Online (LAMJOL), Mongolia Journals Online (MongoliaJOL), Nepal Journals Online (NEPJOL), Sri Lanka Journals Online (SLJOL). Journals Online have quality criteria although they do not have any follow-up control of its enforcement.
About the JOLs
If you haven't found the journal or publisher through the sources above it doesn't mean that they are not legitimate. It might be a new journal and the editor hasn't yet applied for membership or indexing in DOAJ. Presented below is a number of questions you may pose when checking the journal, primarily through its website.
Think. Check. Submit presents a checklist as the one above with questions you should ask yourself before submitting your manuscript. The resource has been developed by, among others, COPE, DOAJ, OASPA, INASP etc.