To be included in WoS: a journal has to have been published for at least three years. Beyond that, the main criteria are: timeliness (must deliver issues on schedule), ethical publishing practices, full text in English (or at least have bibliographic information in English), peer review, and international diversity (are editors and authors from around the world). They also look at the citation history of articles published in the journal.
The full selection criteria are here: https://clarivate.com/webofsciencegroup/journal-evaluation-process-and-selection-criteria/. [Keep scrolling down for additional details.]
If you wish to have a journal added: If you are on a journal editorial board and wish to have your journal considered for inclusion in Web of Science Core Collection - you can submit a request at: https://clarivate.com/webofsciencegroup/solutions/about-publisher-relations/. [Again, keep scrolling down their page for additional links and details.]